Results 21 to 30 of about 332 (184)
Classes of graphs with restricted interval models [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs.
Andrzej Proskurowski, Jan Arne Telle
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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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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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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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Discrete Mathematics & Theoretical Computer Science, 2018 We define a weakly threshold sequence to be a degree sequence $d=(d_1,\dots,d_n)$ of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} - 1$ for all positive $k \leq \max\{i:d_i \geq i-1\}$.
Michael D. Barrus
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Stars in forbidden triples generating a finite set of graphs with minimum degree four
Electronic Journal of Graph Theory and ApplicationsFor a family H of graphs, a graph G is said to be H-free if G contains no member of H as a induced subgraph. Let G4(H) denote the family of connected H-free graphs having minimum degree at least 4.
Takafumi Kotani
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Forbidden subgraphs, stability and hamiltonicity
Discrete Mathematics, 1999 The authors study the stability of some classes of claw-free graphs defined in terms of forbidden subgraphs under the closure operation defined in \textit{Z. Ryjáček} [J. Comb. Theory, Ser. B 70, No.~2, 217-224 (1997; Zbl 0872.05032)]. They characterize all connected graphs \(A\) such that the class of all \(CA\)-free graphs (where \(C\) denotes the ...
Jan Brousek +2 more
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3-Rainbow Index and Forbidden Subgraphs [PDF]
Graphs and Combinatorics, 2017 11 ...
Wenjing Li +2 more
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Toughness, Forbidden Subgraphs, and Hamilton-Connected Graphs
Discussiones Mathematicae Graph Theory, 2022 A graph G is called Hamilton-connected if for every pair of distinct vertices {u, v} of G there exists a Hamilton path in G that connects u and v. A graph G is said to be t-tough if t·ω(G − X) ≤ |X| for all X ⊆ V (G) with ω(G − X) > 1. The toughness of G,
Zheng Wei, Broersma Hajo, Wang Ligong
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