اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the independence number of graphs related to a polarity
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We investigate the independence number of two graphs constructed from a polarity of $mathrm{PG}(2,q)$. For the first graph under consideration, the ErdH{o}s-Renyi graph $ER_q$, we provide an improvement on the known lower bounds on its independence number. In the second part of the paper we consider the ErdH{o}s-Renyi hypergraph of triangles $mathcal{H}_q$. We determine the exact magnitude of the independence number of $mathcal{H}_q$, $q$ even. This solves a problem posed by Mubayi and Williford.
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Let $G=(V,E)$ be a graph and $n$ a positive integer. Let $I_n(G)$ be the abstract simplicial complex whose simplices are the subsets of $V$ that do not contain an independent set of size $n$ in $G$. We study the collapsibility numbers of the complexe
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Let $G$ be a simple graph with maximum degree $Delta(G)$ and chromatic index $chi(G)$. A classic result of Vizing indicates that either $chi(G )=Delta(G)$ or $chi(G )=Delta(G)+1$. The graph $G$ is called $Delta$-critical if $G$ is connected, $chi(G )
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Given a digraph $D$ with $m$ arcs and a bijection $tau: A(D)rightarrow {1, 2, ldots, m}$, we say $(D, tau)$ is an antimagic orientation of a graph $G$ if $D$ is an orientation of $G$ and no two vertices in $D$ have the same vertex-sum under $tau$, wh
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