Monochromatic Hamiltonian t-tight Berge-cycles in hypergraphs

Abstract: In any r-uniform hypergraph H for 2 t r we define an runiform t-tight Berge-cycle of length , denoted by C(r,t) , as a sequence of distinct vertices v1, v2, . . . , v , such that for each set (vi, vi+1, . . . ,vi+t-1) of t consecutive vertices on the cycle, there is an edge Ei of H that contains these t vertices and the edges Ei are all distinct for i, 1 i , where + j j. For t = 2 we get the classical Berge-cycle and for t = r we get the so-called tight cycle. In this note we formulate the following conjecture. For Contract grant sponsor: National Science Foundation; Contract grant number: DMS-0456401; Contract grant sponsor: OTKA; Contract grant number: K68322. Journal of Graph Theory

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Paul Dorbec, Sylvain Gravier, Gábor N. Sárközy
• Keywords: Distinct Vertices, JGT 2008, R-uniform Hypergraph, Runiform T-tight Berge-cycle