Zobrazeno 1 - 10
of 7 954
pro vyhledávání: '"clique number"'
Hyperbolic random graphs inherit many properties that are present in real-world networks. The hyperbolic geometry imposes a scale-free network with a strong clustering coefficient. Other properties like a giant component, the small world phenomena an
Externí odkaz:
http://arxiv.org/abs/2410.11549
Autor:
Girão, António, Insley, Toby
We prove that for each integer $r\geq 2$, there exists a constant $C_r>0$ with the following property: for any $0<\varepsilon \leq 1/2$ and any graph $G$ with clique number at most $r,$ there is a partition of $V(G)$ into at most $(1/\varepsilon)^{C_
Externí odkaz:
http://arxiv.org/abs/2411.19915
Let $\cal H$ be a family of graphs. The Tur\'an number ${\rm ex}(n,{\cal H})$ is the maximum possible number of edges in an $n$-vertex graph which does not contain any member of $\cal H$ as a subgraph. As a common generalization of Tur\'an's theorem
Externí odkaz:
http://arxiv.org/abs/2410.06449
We prove that a hereditary class of graphs is $(\mathsf{tw}, \omega)$-bounded if and only if the induced minors of the graphs from the class form a $(\mathsf{tw}, \omega)$-bounded class.
Externí odkaz:
http://arxiv.org/abs/2410.17979
Autor:
Alali, Amal S.1 (AUTHOR) asalali@pnu.edu.sa, Binyamin, Muhammad Ahsan2 (AUTHOR) ahsanbanyamin@gmail.com, Mehtab, Maria2 (AUTHOR)
Publikováno v:
Symmetry (20738994). Jul2024, Vol. 16 Issue 7, p854. 15p.
WE study the clique number and the chromatic number of generalized Sierpinski graphs in which the base graph is an arbitrary simple graph.
Externí odkaz:
http://arxiv.org/abs/2405.19172
The exact distance $t$-power of a graph $G$, $G^{[\sharp t]}$, is a graph which has the same vertex set as $G$, with two vertices adjacent in $G^{[\sharp t]}$ if and only if they are at distance exactly $t$ in the original graph $G$. We study the cli
Externí odkaz:
http://arxiv.org/abs/2402.00189
We prove that for every integer $t\geq 1$ there exists an integer $c_t\geq 1$ such that every $n$-vertex even-hole-free graph with no clique of size $t$ has treewidth at most $c_t\log{n}$. This resolves a conjecture of Sintiari and Trotignon, who als
Externí odkaz:
http://arxiv.org/abs/2402.14211
Autor:
Dallard, Clément, Krnc, Matjaž, Kwon, O-joung, Milanič, Martin, Munaro, Andrea, Štorgel, Kenny, Wiederrecht, Sebastian
Many recent works address the question of characterizing induced obstructions to bounded treewidth. In 2022, Lozin and Razgon completely answered this question for graph classes defined by finitely many forbidden induced subgraphs. Their result also
Externí odkaz:
http://arxiv.org/abs/2402.11222