Cycles of Given Color Patterns

Y. Manoussakis, M. Spyratos, Zs Tuza

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6 Citations (Scopus)

Abstract

In 2-edge-colored graphs, we define an (s, t)-cycle to be a cycle of length s + t, in which s consecutive edges are in one color and the remaining t edges are in the other color. Here we investigate the existence of (s, t)-cycles, in a 2-edge-colored complete graph Kcn on n vertices. In particular, in the first result we give a complete characterization for the existence of (s, t)-cycles in Kcn with n relatively large with respect to max({s, t}). We also study cycles of length 4 for all possible values' of s and t. Then, we show that Kcn contains an (s, t)-hamiltonian cycle unless it is isomorphic to a specified graph. This extends a result of A. Gyárfás [Journal of Graph Theory, 7 (1983), 131-135]. Finally, we give some sufficient conditions for the existence of (s, 1)-cycles, ∀ s ∈ {2, 3, ⋯, n - 2}.

Original languageEnglish
Pages (from-to)153-162
Number of pages10
JournalJournal of Graph Theory
Volume21
Issue number2
DOIs
Publication statusPublished - Feb 1996

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ASJC Scopus subject areas

  • Geometry and Topology

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