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arXiv · 1507.02463

An extremal problem in proper $(r,p)$-coloring of hypergraphs

Tapas Kumar Mishra·Sudebkumar Prasant Pal
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Abstract

Let $G(V,E)$ be a $k$-uniform hypergraph. A hyperedge $e \in E$ is said to be properly $(r,p)$ colored by an $r$-coloring of vertices in $V$ if $e$ contains vertices of at least $p$ distinct colors in the $r$-coloring. An $r$-coloring of vertices in $V$ is called a {\it strong $(r,p)$ coloring} if every hyperedge $e \in E$ is properly $(r,p)$ colored by the $r$-coloring. We study the maximum number of hyperedges that can be properly $(r,p)$ colored by a single $r$-coloring and the structures that maximizes number of properly $(r,p)$ colored hyperedges.

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Tapas Kumar Mishra, Sudebkumar Prasant Pal. 2015-07-09. An extremal problem in proper $(r,p)$-coloring of hypergraphs. https://arxiv.org/abs/1507.02463

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