Degree versions of the Erdős-Ko-Rado theorem and Erdős hypergraph matching conjecture

DOI10.1016/J.JCTA.2017.03.006zbMATH Open1362.05091arXiv1605.07535OpenAlexW2602080697WikidataQ123014074 ScholiaQ123014074MaRDI QIDQ2397107

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Publication date: 29 May 2017

Published in: (Search for Journal in Brave)

Abstract: We use an algebraic method to prove a degree version of the celebrated ErdH os-Ko-Rado theorem: given $n>2k$, every intersecting $k$-uniform hypergraph $H$ on $n$ vertices contains a vertex that lies on at most $$ edges. This result can be viewed as a special case of the degree version of a well-known conjecture of ErdH{o}s on hypergraph matchings. Improving the work of Bollob'as, Daykin, and ErdH os from 1976, we show that given integers $n,k,s$ with $nge3k^{2}s$, every $k$-uniform hypergraph $H$ on $n$ vertices with minimum vertex degree greater than $$ contains $s$ disjoint edges.

Full work available at URL: https://arxiv.org/abs/1605.07535

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