Results 11 to 20 of about 8,766 (207)
Clique immersions and independence number [PDF]
European Journal of Combinatorics, 2022 13 pages, 1 figure.
Bustamante, Sebastián +3 more
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Minimum Clique Number, Chromatic Number, and Ramsey Numbers [PDF]
The Electronic Journal of Combinatorics, 2012 Let $Q(n,c)$ denote the minimum clique number over graphs with $n$ vertices and chromatic number $c$. We investigate the asymptotics of $Q(n,c)$ when $n/c$ is held constant. We show that when $n/c$ is an integer $\alpha$, $Q(n,c)$ has the same growth order as the inverse function of the Ramsey number $R(\alpha+1,t)$ (as a function of $t$). Furthermore,
Gaku Liu
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Bounds on the Clique and the Independence Number for Certain Classes of Graphs [PDF]
MathematicsIn this paper, we study the class of graphs Gm,n that have the same degree sequence as two disjoint cliques Km and Kn, as well as the class G¯m,n of the complements of such graphs.
Valentin E. Brimkov, Reneta P. Barneva
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Treewidth versus clique number. II. Tree-independence number
Journal of Combinatorial Theory, Series B, 2023 In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call $(\mathrm{tw},ω)$-bounded. While $(\mathrm{tw},ω)$-bounded graph classes are known to enjoy some good algorithmic properties related to clique and coloring problems, it is an interesting open problem ...
Dallard, Clément +2 more
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Small clique number graphs with three trivial critical ideals
Special Matrices, 2018 The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. Previously, they have been used in the understanding and characterizing of the graphs with critical group with few invariant factors ...
Alfaro Carlos A., Valencia Carlos E.
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Packing chromatic number versus chromatic and clique number [PDF]
Aequationes mathematicae, 2017 The packing chromatic number $ _ (G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\in [k]$, where each $V_i$ is an $i$-packing. In this paper, we investigate for a given triple $(a,b,c)$ of positive integers whether there exists a graph $G$ such that $ (G) = a$, $ (G) = b$, and $
Boštjan Brešar +3 more
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Cluster deletion and clique partitioning in graphs with bounded clique number [PDF]
14 pages, 3 ...
Galesi, Nicola +2 more
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Rainbow Turán number of clique subdivisions
European Journal of Combinatorics, 2023 We show that for any integer $t\geq 2$, every properly edge-coloured graph on $n$ vertices with more than $n^{1+o(1)}$ edges contains a rainbow subdivision of $K_t$. Note that this bound on the number of edges is sharp up to the $o(1)$ error term. This is a rainbow analogue of some classical results on clique subdivisions and extends some results on ...
Jiang, Tao +2 more
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Some Chemistry Indices of Clique-Inserted Graph of a Strongly Regular Graph
Complexity, 2021 In this paper, we give the relation between the spectrum of strongly regular graph and its clique-inserted graph. The Laplacian spectrum and the signless Laplacian spectrum of clique-inserted graph of strongly regular graph are calculated.
Chun-Li Kan +3 more
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General multiplicative Zagreb indices of graphs with given clique number [PDF]
Opuscula Mathematica, 2019 We obtain lower and upper bounds on general multiplicative Zagreb indices for graphs of given clique number and order. Bounds on the basic multiplicative Zagreb indices and on the multiplicative sum Zagreb index follow from our results. We also determine
Tomáš Vetrík, Selvaraj Balachandran
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