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Forbidden subgraph decomposition
Discrete Mathematics, 2002 no ...
Rusu, Irena, Spinrad, Jeremy P.
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On Minrank and Forbidden Subgraphs [PDF]
ACM Transactions on Computation Theory, 2019 The minrank over a field F of a graph G on the vertex set { 1,2,… , n } is the minimum possible rank of a matrix M ∈ F n × n such that M
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Upward-closed hereditary families in the dominance order [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the ...
Michael D. Barrus, Jean A. Guillaume
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Forbidden subgraphs for chorded pancyclicity
Discrete Mathematics, 2017 We call a graph $G$ pancyclic if it contains at least one cycle of every possible length $m$, for $3\le m\le |V(G)|$. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length $4, 5, \ldots, |V(G)|
Megan Cream +2 more
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The graph grabbing game on {0,1}-weighted graphs
Results in Applied Mathematics, 2019 The graph grabbing game is a two-player game on a weighted connected graph in which two players, Alice and Bob, alternatively remove non-cut vertices one by one to gain the weights on them.
Soogang Eoh, Jihoon Choi
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Complexity Framework For Forbidden Subgraphs.
CoRR, 2022 For any finite set H={H1,…,Hp} of graphs, a graph is H-subgraph-free if it does not contain any of H1,…,Hp as a subgraph. Similar to known meta-classifications for the minor and topological minor relations, we give a meta-classification for the subgraph relation.
Matthew Johnson 0002 +6 more
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Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Discussiones Mathematicae Graph Theory, 2021 Let γ(G) and γe(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture:
Chen Xue-Gang, Wang Yu-Feng, Wu Xiao-Fei
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Colouring graphs with forbidden bipartite subgraphs
Combinatorics, Probability and Computing, 2022 AbstractA conjecture of Alon, Krivelevich and Sudakov states that, for any graph $F$ , there is a constant $c_F \gt 0$ such that if $G$ is an $F$ -free graph of maximum degree $\Delta$ , then $\chi\!(G) \leqslant c_F \Delta/ \log\!\Delta$ . Alon, Krivelevich and Sudakov verified this conjecture for a class of graphs $F$ that includes all ...
James Anderson +2 more
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Forbidden subgraphs in connected graphs
Theoretical Computer Science, 2004 Given a set $ξ=\{H_1,H_2,...\}$ of connected non acyclic graphs, a $ξ$-free graph is one which does not contain any member of $% ξ$ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let ${\gr{W}}_{k,ξ}$ be theexponential generating function (EGF for brief) of connected $ξ$-free graphs of ...
Ravelomanana, Vlady, Loÿs, Thimonier
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Electronic Journal of Graph Theory and Applications, 2018 We find the structure of graphs that have no C4, $\overline{C}_4$, C5, S3, chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $\overline{C_4}$, S3, chair and co-chair and the structure of the graphs ...
Salman Ghazal
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