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Semi-strict Chordality of Digraphs Graphs Comb. (IF 0.7) Pub Date : 2024-04-17 Jing Huang, Ying Ying Ye
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Computing the Number and Average Size of Connected Sets in Planar 3-Trees Graphs Comb. (IF 0.7) Pub Date : 2024-04-17 Zuwen Luo, Kexiang Xu
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Gallai–Ramsey Multiplicity Graphs Comb. (IF 0.7) Pub Date : 2024-04-14 Yaping Mao
Given two graphs G and H, the general k-colored Gallai–Ramsey number \({\text {gr}}_k(G:H)\) is defined to be the minimum integer m such that every k-coloring of the complete graph on m vertices contains either a rainbow copy of G or a monochromatic copy of H. Interesting problems arise when one asks how many such rainbow copy of G and monochromatic copy of H must occur. The Gallai–Ramsey multiplicity
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Minimal Obstructions for Polarity, Monopolarity, Unipolarity and (s, 1)-Polarity in Generalizations of Cographs Graphs Comb. (IF 0.7) Pub Date : 2024-04-09 Fernando Esteban Contreras-Mendoza, César Hernández-Cruz
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On the Existence of Small Strictly Neumaier Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-04-08 Aida Abiad, Maarten De Boeck, Sjanne Zeijlemaker
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Stability of Generalized Turán Number for Linear Forests Graphs Comb. (IF 0.7) Pub Date : 2024-04-08 Yisai Xue, Yichong Liu, Liying Kang
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A Matrix for Counting Paths in Acyclic Colored Digraphs Graphs Comb. (IF 0.7) Pub Date : 2024-04-08 Sudip Bera
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The primality graph of critical 3-hypergraphs Graphs Comb. (IF 0.7) Pub Date : 2024-04-06
Abstract Given a 3-hypergraph H, a subset M of V(H) is a module of H if for each \(e\in E(H)\) such that \(e\cap M\ne \emptyset \) and \(e{\setminus } M\ne \emptyset \) , there exists \(m\in M\) such that \(e\cap M=\{m\}\) and for every \(n\in M\) , we have \((e{\setminus }\{m\})\cup \{n\}\in E(H)\) . For example, \(\emptyset \) , V(H) and \(\{v\}\) , where \(v\in V(H)\) , are modules of H, called
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On the Edge-Erdős–Pósa Property of Ladders Graphs Comb. (IF 0.7) Pub Date : 2024-04-05 Raphael Steck, Arthur Ulmer
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Planar Graphs with the Maximum Number of Induced 4-Cycles or 5-Cycles Graphs Comb. (IF 0.7) Pub Date : 2024-04-05 Michael Savery
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Path Saturation Game on Six Vertices Graphs Comb. (IF 0.7) Pub Date : 2024-04-03 Paul Balister, Ali Dogan
Given a family \(\mathcal {F}\) of graphs, we say that a graph G is \(\mathcal {F}\)-saturated if G does not contain any member of \(\mathcal {F}\), but for any edge \(e\in E(\overline{G})\) the graph \(G+e\) does contain a member of \(\mathcal {F}\). The \(\mathcal {F}\)-saturation game is played by two players starting with an empty graph and adding an edge on their turn without making a member of
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Using Euler’s Formula to Find the Lower Bound of the Page Number Graphs Comb. (IF 0.7) Pub Date : 2024-04-03 Bin Zhao, Peng Li, Jixiang Meng, Yuepeng Zhang
The concept of book embedding, originating in computer science, has found extensive applications in various problem domains. A book embedding of a graph G involves arranging the vertices of G in an order along a line and assigning the edges to one or more half-planes. The page number of a graph is the smallest possible number of half-planes for any book embedding of the graph. Determining the page
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Some Results on the Rainbow Vertex-Disconnection Colorings of Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-04-02 Yindi Weng
Let G be a nontrivial connected and vertex-colored graph. A vertex subset X is called rainbow if any two vertices in X have distinct colors. The graph G is called rainbow vertex-disconnected if for any two vertices x and y of G, there exists a vertex subset S such that when x and y are nonadjacent, S is rainbow and x and y belong to different components of \(G-S\); whereas when x and y are adjacent
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Removable Edges in Claw-Free Bricks Graphs Comb. (IF 0.7) Pub Date : 2024-04-02
Abstract An edge e in a matching covered graph G is removable if \(G-e\) is matching covered. Removable edges were introduced by Lovász and Plummer in connection with ear decompositions of matching covered graphs. A brick is a non-bipartite matching covered graph without non-trivial tight cuts. The importance of bricks stems from the fact that they are building blocks of matching covered graphs. Lovász
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Cycle Isolation of Graphs with Small Girth Graphs Comb. (IF 0.7) Pub Date : 2024-03-26 Gang Zhang, Baoyindureng Wu
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Extremal Edge General Position Sets in Some Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-03-26
Abstract A set of edges \(X\subseteq E(G)\) of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number \({\textrm{gp}}_{\textrm{e}}(G)\) of G is the cardinality of a largest edge general position set in G. Graphs G with \({\textrm{gp}}_{{\textrm{e}}}(G) = |E(G)| - 1\) and with \({\textrm{gp}}_{{\textrm{e}}}(G) = 3\) are respectively
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Neighborhood Balanced Colorings of Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-03-26 Bryan Freyberg, Alison Marr
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On Non-degenerate Berge–Turán Problems Graphs Comb. (IF 0.7) Pub Date : 2024-03-26 Dániel Gerbner
Given a hypergraph \({{\mathcal {H}}}\) and a graph G, we say that \({{\mathcal {H}}}\) is a Berge-G if there is a bijection between the hyperedges of \({{\mathcal {H}}}\) and the edges of G such that each hyperedge contains its image. We denote by \(\textrm{ex}_k(n,Berge- F)\) the largest number of hyperedges in a k-uniform Berge-F-free graph. Let \(\textrm{ex}(n,H,F)\) denote the largest number of
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Strongly Regular Graphs from Pseudocyclic Association Schemes Graphs Comb. (IF 0.7) Pub Date : 2024-03-26 Koji Momihara, Sho Suda
In this paper, we give a construction of strongly regular graphs from pseudocyclic association schemes, which is a common generalization of two constructions given by Fujisaki (2004). Furthermore, we prove that the pseudocyclic association scheme arising from the action of PGL(2, q) to the set of exterior lines in PG(2, q), called the elliptic scheme, under the assumption that \(q=2^m\) with m an odd
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A Note on Internal Partitions: The 5-Regular Case and Beyond Graphs Comb. (IF 0.7) Pub Date : 2024-03-23 Pál Bärnkopf, Zoltán Lóránt Nagy, Zoltán Paulovics
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Self-Orthogonal Codes from Deza Graphs, Normally Regular Digraphs and Deza Digraphs Graphs Comb. (IF 0.7) Pub Date : 2024-03-21 Dean Crnković, Andrea Švob
In this paper, we give constructions of self-orthogonal codes from orbit matrices of Deza graphs, normally regular digraphs and Deza digraphs in terms of a definition given by Wang and Feng. These constructions can also be applied to adjacency matrices of the mentioned graphs. Since a lot of constructions of Deza graphs, normally regular digraphs and Deza digraphs in the sense of Wang and Feng have
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The Existence of a Path with Two Blocks in Digraphs Graphs Comb. (IF 0.7) Pub Date : 2024-03-12 Amine El Sahili, Maidoun Mortada, Sara Nasser
We give a new elementary proof of El Sahili conjecture El Sahili (Discrete Math 287:151–153, 2004) stating that any n-chromatic digraph D, with \(n\ge 4\), contains a path with two blocks of order n.
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A Note on the Gyárfás–Sumner Conjecture Graphs Comb. (IF 0.7) Pub Date : 2024-03-08 Tung Nguyen, Alex Scott, Paul Seymour
The Gyárfás–Sumner conjecture says that for every tree T and every integer \(t\ge 1\), if G is a graph with no clique of size t and with sufficiently large chromatic number, then G contains an induced subgraph isomorphic to T. This remains open, but we prove that under the same hypotheses, G contains a subgraph H isomorphic to T that is “path-induced”; that is, for some distinguished vertex r, every
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The Spectral Radius, Maximum Average Degree and Cycles of Consecutive Lengths of Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-03-05 Wenqian Zhang
In this paper, we study the relationship between spectral radius and maximum average degree of graphs. By using this relationship and the previous technique of Li and Ning in (J Graph Theory 103:486–492, 2023), we prove that, for any given positive number \(\varepsilon <\frac{1}{3}\), if n is a sufficiently large integer, then any graph G of order n with \(\rho (G)>\sqrt{\left\lfloor \frac{n^{2}}{4}\right\rfloor
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On Restricted Intersections and the Sunflower Problem Graphs Comb. (IF 0.7) Pub Date : 2024-03-04 Jeremy Chizewer
A sunflower with r petals is a collection of r sets over a ground set X such that every element in X is in no set, every set, or exactly one set. Erdős and Rado [5] showed that a family of sets of size n contains a sunflower if there are more than \(n!(r-1)^n\) sets in the family. Alweiss et al. [1] and subsequently, Rao [7] and Bell et al. [2] improved this bound to \((O(r \log n))^n\). We study the
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Infinite Families of k-Vertex-Critical ( $$P_5$$ , $$C_5$$ )-Free Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-02-25 Ben Cameron, Chính Hoàng
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Planar Turán Numbers of Cubic Graphs and Disjoint Union of Cycles Graphs Comb. (IF 0.7) Pub Date : 2024-02-25
Abstract The planar Turán number of a graph H, denoted by \(ex_{_\mathcal {P}}(n,H)\) , is the maximum number of edges in a planar graph on n vertices without containing H as a subgraph. This notion was introduced by Dowden in 2016 and has attracted quite some attention since then; those work mainly focus on finding \(ex_{_\mathcal {P}}(n,H)\) when H is a cycle or Theta graph or H has maximum degree
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Weak Dynamic Coloring of Planar Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-02-24 Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger
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Borodin–Kostochka Conjecture Holds for Odd-Hole-Free Graphs Graphs Comb. (IF 0.7) Pub Date : 2024-02-10 Rong Chen, Kaiyang Lan, Xinheng Lin, Yidong Zhou
The Borodin–Kostochka Conjecture states that for a graph G, if \(\Delta (G)\ge 9\), then \(\chi (G)\le \max \{\Delta (G)-1,\omega (G)\}\). In this paper, we prove the Borodin–Kostochka Conjecture holding for odd-hole-free graphs.
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Parallel Connectivity in Edge-Colored Complete Graphs: Complexity Results Graphs Comb. (IF 0.7) Pub Date : 2024-02-10 Rachid Saad
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On Inducing Degenerate Sums Through 2-Labellings Graphs Comb. (IF 0.7) Pub Date : 2024-02-09 Julien Bensmail, Hervé Hocquard, Pierre-Marie Marcille
We deal with a variant of the 1–2–3 Conjecture introduced by Gao, Wang, and Wu (Graphs Combin 32:1415–1421, 2016) . This variant asks whether all graphs can have their edges labelled with 1 and 2 so that when computing the sums of labels incident to the vertices, no monochromatic cycle appears. In the aforementioned seminal work, the authors mainly verified their conjecture for a few classes of graphs
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Infinite Ramsey-Minimal Graphs for Star Forests Graphs Comb. (IF 0.7) Pub Date : 2024-02-09 Fawwaz Fakhrurrozi Hadiputra, Valentino Vito
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Multipermutations and Stirling Multipermutations Graphs Comb. (IF 0.7) Pub Date : 2024-02-07 Richard A. Brualdi, Geir Dahl
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Lattice Path Bicircular Matroids Graphs Comb. (IF 0.7) Pub Date : 2024-02-07
Abstract Lattice path matroids and bicircular matroids are two well-known classes of transversal matroids. In the seminal work of Bonin and de Mier about structural properties of lattice path matroids, the authors claimed that lattice path matroids significantly differ from bicircular matroids. Recently, it was proved that all cosimple lattice path matroids have positive double circuits, while it was
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The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions Graphs Comb. (IF 0.7) Pub Date : 2024-02-06 Sarah Allred, Emelie Curl, Shaun Fallat, Shahla Nasserasr, Houston Schuerger, Ralihe R. Villagrán, Prateek K. Vishwakarma
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A Novel Count of the Spanning Trees of a Cube Graphs Comb. (IF 0.7) Pub Date : 2024-01-28 Thomas W. Mattman
Using the special value at \(u=1\) of the Artin-Ihara L-function, we give a short proof of the count of the number of spanning trees in the n-cube.
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The Oriented Diameter of Graphs with Given Connected Domination Number and Distance Domination Number Graphs Comb. (IF 0.7) Pub Date : 2024-01-28 Peter Dankelmann, Jane Morgan, Emily Rivett-Carnac
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Crossing and intersecting families of geometric graphs on point sets Graphs Comb. (IF 0.7) Pub Date : 2024-01-25 J. L. Álvarez-Rebollar, J. Cravioto-Lagos, N. Marín, O. Solé-Pi, J. Urrutia
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A Construction of Optimal 1-Spontaneous Emission Error Designs Graphs Comb. (IF 0.7) Pub Date : 2024-01-19 Junling Zhou, Na Zhang
A t-spontaneous emission error design, denoted by t-(v, k; m) SEED or t-SEED in short, is a system \({{\mathcal {B}}}\) of k-subsets of a v-set V with a partition \({{\mathcal {B}}}_1,\mathcal{B}_2,\ldots ,{{\mathcal {B}}}_{m}\) of \({{\mathcal {B}}}\) satisfying \({{|\{B\in {\mathcal {B}}_i:\, E \subseteq B\}|}\over {|{\mathcal {B}}_i|}}=\mu _E \) for any \(1\le i\le m\) and \(E\subseteq V\), \(|E|\le
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Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric Graphs Comb. (IF 0.7) Pub Date : 2024-01-19 Mansoor Davoodi, Ashkan Safari
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Compatible Spanning Circuits and Forbidden Induced Subgraphs Graphs Comb. (IF 0.7) Pub Date : 2024-01-19 Zhiwei Guo, Christoph Brause, Maximilian Geißer, Ingo Schiermeyer
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Fixing Numbers of Graphs with Symmetric and Generalized Quaternion Symmetry Groups Graphs Comb. (IF 0.7) Pub Date : 2024-01-19 Christina Graves, L.-K. Lauderdale
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Equality of Ordinary and Symbolic Powers of Some Classes of Monomial Ideals Graphs Comb. (IF 0.7) Pub Date : 2024-01-19 Kanoy Kumar Das
In this article, our aim is to extend the class of monomial ideals for which symbolic and ordinary powers coincide. This property has been characterized for the class of edge ideals of simple graphs, and in this article, we study a completely new class of monomial ideals associated to simple graphs, namely the class of generalized edge ideals. We give a complete description of the primary components
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Coloring of Graphs Avoiding Bicolored Paths of a Fixed Length Graphs Comb. (IF 0.7) Pub Date : 2024-01-11 Alaittin Kırtışoğlu, Lale Özkahya
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Signed Ramsey Numbers Graphs Comb. (IF 0.7) Pub Date : 2023-12-28 Mohammed A. Mutar, Vaidy Sivaraman, Daniel Slilaty
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Erdős–Hajnal Problem for H-Free Hypergraphs Graphs Comb. (IF 0.7) Pub Date : 2023-12-28 Danila Cherkashin, Alexey Gordeev, Georgii Strukov
This paper deals with the minimum number \(m_H(r)\) of edges in an H-free hypergraph with the chromatic number more than r. We show how bounds on Ramsey and Turán numbers imply bounds on \(m_H(r)\).
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Four-vertex traces of finite sets Graphs Comb. (IF 0.7) Pub Date : 2023-12-23 Peter Frankl, Jian Wang
Let \([n]=X_1\cup X_2\cup X_3\) be a partition with \(\lfloor \frac{n}{3}\rfloor \le |X_i|\le \lceil \frac{n}{3}\rceil \) and define \({\mathcal {G}}=\{G\subset [n]:|G\cap X_i|\le 1, 1\le i\le 3\}\). It is easy to check that the trace \({\mathcal {G}}_{\mid Y}:=\{G\cap Y:G\in {\mathcal {G}}\}\) satisfies \(|{\mathcal {G}}_{\mid Y}|\le 12\) for all 4-sets \(Y\subset [n]\). In the present paper, we prove
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Weak-Dynamic Coloring of Graphs Beyond-Planarity Graphs Comb. (IF 0.7) Pub Date : 2023-12-23 Weichan Liu, Guiying Yan
A weak-dynamic coloring of a graph is a vertex coloring (not necessarily proper) in such a way that each vertex of degree at least two sees at least two colors in its neighborhood. It is proved that the weak-dynamic chromatic number of the class of k-planar graphs (resp. IC-planar graphs) is equal to (resp. at most) the chromatic number of the class of 2k-planar graphs (resp. 1-planar graphs), and
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Some New Constructions of Difference Systems of Sets Graphs Comb. (IF 0.7) Pub Date : 2023-12-23 Shuyu Shen, Jingjun Bao
Difference systems of sets (DSSs) are combinatorial structures introduced by Levenshtein, which are a generalization of cyclic difference sets and arise in connection with code synchronization. In this paper, we describe four direct constructions of optimal DSSs from finite projective geometries and present a recursive construction of DSSs by extending the known construction. As a consequence, new
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The Maximum 4-Vertex-Path Packing of a Cubic Graph Covers At Least Two-Thirds of Its Vertices Graphs Comb. (IF 0.7) Pub Date : 2023-12-20 Wenying Xi, Wensong Lin
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Tashkinov-Trees: An Annotated Proof Graphs Comb. (IF 0.7) Pub Date : 2023-12-14 András Sebő
Tashkinov-trees have been used as a tool for proving bounds on the chromatic index, and are becoming a fundamental tool for edge-coloring. Was its publication in a language different from English an obstacle for the accessibility of a clean and complete proof of Tashkinov’s fundamental theorem? Tashkinov’s original, Russian paper offers a clear presentation of this theorem and its proof. The theorem
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Turán Numbers of Several Bipartite Graphs Graphs Comb. (IF 0.7) Pub Date : 2023-12-14 Ye Wang, Yusheng Li, Yan Li
For graphs \(H_1,H_2,\dots ,H_k\), the k-color Turán number \(ex(n,H_1,H_2,\dots ,H_k)\) is the maximum number of edges in a k-colored graph of order n that does not contain monochromatic \(H_i\) in color i as a subgraph, where \(1\le i\le k\). In this note, we show that if \(H_i\) is a bipartite graph with at least two edges for \(1\le i\le k\), then \(ex(n,H_1,H_2,\dots ,H_k)=(1+o(1))\sum _{i=1}^kex(n
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On the Turán Number of $$K_m \vee C_{2k-1}$$ Graphs Comb. (IF 0.7) Pub Date : 2023-12-04 Jingru Yan
Given a graph H and a positive integer n, the Turán number of H of the order n, denoted by ex(n, H), is the maximum size of a simple graph of order n that does not contain H as a subgraph. Given graphs G and H, \(G \vee H\) denotes the join of G and H. In this paper, we prove \(ex(n, K_m \vee C_{2k-1}) = \left\lfloor \frac{(m+1)n^2}{2(m+2)}\right\rfloor \) for \(n\ge 2(m+2)k-3(m+2)-1\).
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Complexity of Total Dominator Coloring in Graphs Graphs Comb. (IF 0.7) Pub Date : 2023-11-28 Michael A. Henning, Kusum, Arti Pandey, Kaustav Paul
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$$l_{1}$$ -embeddability of shifted quadrilateral cylinder graphs Graphs Comb. (IF 0.7) Pub Date : 2023-11-29 Guangfu Wang, Zhikun Xiong, Lijun Chen
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Size Gallai–Ramsey Number Graphs Comb. (IF 0.7) Pub Date : 2023-11-23 Yaping Mao
The size Ramsey number \({\hat{\textrm{r}}}(G,H)\) of two graphs G, H, introduced by Erdös et al., is defined as \({\hat{\textrm{r}}}(G,H)=\min \{|E(F)|:F\longrightarrow (G,H)\}\). Recently, Gallai–Ramsey number \(\textrm{gr}_k\) has been studied a lot. In this paper, we introduce the concept of size Gallai–Ramsey number (Simply, SGR number) of graphs. Given two graphs G and H, the size Gallai–Ramsey