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Cops and Robbers on Graphs with a Set of Forbidden Induced Subgraphs [PDF]
Theoretical Computer Science, 2018 It is known that the class of all graphs not containing a graph $H$ as an induced subgraph is cop-bounded if and only if $H$ is a forest whose every component is a path.
Masood Masjoody, L. Stacho
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Forbidden Subgraph Problems with Predictions [PDF]
International Symposium on Mathematical Foundations of Computer ScienceIn the Online Delayed Connected H-Node-Deletion Problem, an unweighted graph is revealed vertex by vertex and it must remain free of any induced copies of a specific connected induced forbidden subgraph H at each point in time.
Hans-Joachim Böckenhauer +3 more
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, 2017 Beineke in 1969 characterized the class of line graphs in terms of forbidden induced subgraphs. For given graphs G and H, G is said to be H-free if G does not contain an induced subgraph isomorphic to H. Analogously, for graphs H1, . . .
Přemysl Holub
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Clique-Width of Graph Classes Defined by Two Forbidden Induced Subgraphs [PDF]
The Computer Journal, 2014 If a graph has no induced subgraph isomorphic to any graph in a finite family $$\{H_1,\ldots ,H_p\}$$, it is said to be $$H_1,\ldots ,H_p$$-free. The class of $$H$$-free graphs has bounded clique-width if and only if $$H$$ is an induced subgraph of the 4-
Konrad K. Dabrowski, D. Paulusma
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Near-complete multipartite graphs and forbidden induced subgraphs [PDF]
Discrete Mathematics, 1999 A proper vertex k-coloring C1,C2,…,Ck of a graph G is called l-bounded (l⩾0) if |Ci⧹N(u)|⩽l for each i=1,2,…,k and each vertex u∈VG⧹Ci, where N(u) is the neighborhood of u. Let C(k,l) be the class of all graphs having an l-bounded k-coloring (k⩾1 and l⩾0)
Zverovich, Igor E.
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On characterizing game-perfect graphs by forbidden induced subgraphs [PDF]
Contributions to Discrete Mathematics, 2012 A graph $G$ is called $g$-perfect if, for any induced subgraph $H$ of $G$, the game chromatic number of $H$ equals the clique number of $H$. A graph $G$ is called $g$-col-perfect if, for any induced subgraph $H$ of $G$, the game coloring number of $H ...
Andres, Stephan Dominique
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List-3-Coloring Ordered Graphs with a Forbidden Induced Subgraph [PDF]
SIAM Journal on Discrete Mathematics, 2022 The List-3-Coloring Problem is to decide, given a graph $G$ and a list $L(v)\subseteq \{1,2,3\}$ of colors assigned to each vertex $v$ of $G$, whether $G$ admits a proper coloring $\phi$ with $\phi(v)\in L(v)$ for every vertex $v$ of $G$, and the $3 ...
Sepehr Hajebi, Yanjia Li, S. Spirkl
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Small bipartite subgraph polytopes [PDF]
, 2010 We compute a complete linear description of the bipartite subgraph polytope, for up to seven nodes, and a conjectured complete description for eight nodes.
Galli, L, Letchford, A N
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Forbidden Induced Subgraphs and the Łoś–Tarski Theorem [PDF]
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021 AbstractLet $\mathscr {C}$ be a class of finite and infinite graphs that is closed under induced subgraphs. The well-known Łoś–Tarski Theorem from classical model theory implies that $\mathscr {C}$ is definable in first-order logic by a sentence $\varphi $ if and only if $\mathscr {C}$ has a finite set of forbidden induced finite subgraphs ...
Chen, Yijia, Flum, Jörg
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A semi-induced subgraph characterization of upper domination perfect graphs [PDF]
, 1999 Let β(G) and Γ(G) be the independence number and the upper domination number of a graph G, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of
Zverovich, Vadim +3 more
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