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Clique-Number of Timbral Graphs
We study the clique-number of the timbral graphs Tn,k,ℓ. The vertex set of Tn,k,ℓ is the set of all words of length k built on an alphabet of n symbols and two vertices are adjacent when they agree in exactly ℓ coordinates. We provide lower and upper bounds for the general case and determine ω(Tn,k,1) when k−1 ≤ n is a prime power, showing the ...
Márcia R. Cerioli +2 more
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Clique Chromatic Numbers of Intersection Graphs
Mathematical Notes, 2019The clique chromatic number \(\chi_c(G)\) of a graph \(G\) is the minimum \(k\) for which there exists a \(k\)-coloring of the vertices of \(G\) such that all inclusion-maximal cliques, except for isolated vertices, are non-monochromatic. When \([n]=\{1,2,\dots,n\}\), \(G(n,r,s)\) is the graph whose vertex-set is \(\binom{[n]}{r}\), and whose edges ...
Zakharov, D. A., Raigorodskii, A. M.
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Clique-transversal number of graphs whose clique-graphs are trees
Journal of Shanghai University (English Edition), 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang, Zuosong, Shan, Erfang
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Independence number and clique minors
Journal of Graph Theory, 2007AbstractThe Hadwiger number ${h}({G})$ of a graph G is the maximum integer t such that ${K}_{t}$ is a minor of G. Since $\chi({G})\cdot\alpha({G})\geq |{G}|$, Hadwiger's conjecture implies that ${h}({G})\cdot \alpha({G})\geq |{G}|$, where $\alpha({G})$ and $|{G}|$ denote the independence number and the number of vertices of G, respectively.
Kawarabayashi, Ken Ichi, Song, Zi Xia
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The Clique Numbers of Regular Graphs
Graphs and Combinatorics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Relative Clique Number of Planar Signed Graphs
Discrete Applied Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Das, Sandip +3 more
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CLIQUE NUMBERS OF PALEY GRAPHS
Quaestiones Mathematicae, 1988Abstract The clique number of the Paley graph G(q), where q, is a prime power with q ≡ 1 (mod 4) is known to be Jq, when q, is a square. When q, is a non-square the problem of finding a formula for the clique number seems to be a hard one although its value has been obtained by computer search for prime values of q, satisfying 5 ⋚ q, ⋚ 1601.
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