A Degree Sequence Strengthening of the Vertex Degree Threshold for a Perfect Matching in 3-Uniform Hypergraphs
نویسندگان
چکیده
The study of asymptotic minimum degree thresholds that force matchings and tilings in hypergraphs is a lively area research combinatorics. A key breakthrough this was result H\`{a}n, Person Schacht who proved the vertex threshold for perfect matching an $n$-vertex $3$-graph $\left(\frac{5}{9}+o(1)\right)\binom{n}{2}$. In paper we improve on result, giving family sequence results, all which imply Schacht, additionally allow one third vertices to have $\frac{1}{9}\binom{n}{2}$ below threshold. Furthermore, show is, some sense, tight.
منابع مشابه
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2022
ISSN: ['1095-7146', '0895-4801']
DOI: https://doi.org/10.1137/20m1364825