Some lower bounds for the \(L\)-intersection number of graphs

zbMATH Open1373.05124arXiv1211.0328MaRDI QIDQ2412186

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Publication date: 25 October 2017

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Abstract: For a set of non-negative integers $L$, the $L$-intersection number of a graph is the smallest number $l$ for which there is an assignment on the vertices to subsets $A_{v}subseteq1,dots,l$, such that every two vertices $u,v$ are adjacent if and only if $|A_{u}cap{A}_v|inL$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the vertices in different parts. In this paper, some lower bounds for the (bipartite) $L$-intersection number of a graph for various types $L$ in terms of the minimum rank of graph are obtained.

Full work available at URL: https://arxiv.org/abs/1211.0328

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