Anti-Ramsey number of matchings in hypergraphs


Ozkahya L., Young M.

DISCRETE MATHEMATICS, vol.313, no.20, pp.2359-2364, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 313 Issue: 20
  • Publication Date: 2013
  • Doi Number: 10.1016/j.disc.2013.06.015
  • Journal Name: DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2359-2364
  • Hacettepe University Affiliated: Yes

Abstract

A k-matching in a hypergraph is a set of k edges such that no two of these edges intersect. The anti-Ramsey number of a k-matching in a complete s-uniform hypergraph H on n vertices, denoted by ar(n, s, k), is the smallest integer c such that in any coloring of the edges of H with exactly c colors, there is a k-matching whose edges have distinct colors. The Turan number, denoted by ex(n, s, k), is the the maximum number of edges in an s-uniform hypergraph on n vertices with no k-matching. For k >= 3, we conjecture that if n > sk, then ar(n, s, k) = ex(n, s, k 1) + 2. Also, if n = sk, then ar(n, s, k) =