A note on the linear cycle cover conjecture of Gyárfás and Sárközy

Ergemlidze, Beka and Győri, Ervin and Methuku, Abhishek (2018) A note on the linear cycle cover conjecture of Gyárfás and Sárközy. ELECTRONIC JOURNAL OF COMBINATORICS, 25 (2). ISSN 1097-1440

Preview

Text 7329-PDFfile-24444-2-10-20180516.pdf Download (186kB) | Preview

Abstract

A linear cycle in a 3-uniform hypergraph H is a cyclic sequence of hyperedges such that any two consecutive hyperedges intersect in exactly one element and non-consecutive hyperedges are disjoint. Let α(H) denote the size of a largest independent set of H. We show that the vertex set of every 3-uniform hypergraph H can be covered by at most α(H) edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of Gyárfás and Sárközy. © The authors.

Actions (login required)

Edit Item