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On the Linear Cycle Cover Conjecture of Gy\'arf\'as and S\'ark\'ozy
- Publication Year :
- 2016
-
Abstract
- A linear cycle in a hypergraph $H$ is a cyclic sequence of hyperedges such that two consecutive hyperedges intersect in exactly one element and two nonconsecutive hyperedges are disjoint and $\alpha(H)$ denotes the size of a largest independent set of $H$. In this note, we show that the vertex set of every $3$-uniform hypergraph $H$ can be covered by at most $\alpha(H)$ pairwise edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of Gy\'arf\'as and S\'ark\"ozy.
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1609.04761
- Document Type :
- Working Paper