Abstract
A k-uniform tight cycle is a k-uniform hypergraph with a cyclic ordering of its vertices such that its edges are all the sets of size k formed by k consecutive vertices in the ordering. We prove that every red-blue edge-coloured Kn(4) contains a red and a blue tight cycle that are vertex-disjoint and together cover n−o(n) vertices. Moreover, we prove that every red-blue edge-coloured Kn(5) contains four monochromatic tight cycles that are vertex-disjoint and together cover n−o(n) vertices.
Original language | English |
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Article number | P1.13 |
Number of pages | 36 |
Journal | Electronic Journal of Combinatorics |
Volume | 30 |
Issue number | 1 |
DOIs | |
Publication status | Published - 13 Jan 2023 |