Cycles containing matchings and pairwise compatible euler tours

Bill Jackson, Nicholas C. Wormald

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11 Citations (Scopus)


Let M be a matching in a graph G such that d(x) + d(y) ≥ |G| for all pairs of independent vertices x and y of G that are incident with M. We determine a necessary and sufficient condition for M to be contained in a cycle of G. This extends results of Häggkvist and Berman, and implies that if M is a 1‐factor of G and |G|  0 (mod 4), then M is contained in a Hamilton cycle of G. We use our results to deduce that an eulerian graph of minimum degree 2k contains k pairwise compatible Euler tours.

Original languageEnglish
Pages (from-to)127-138
Number of pages12
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - 1990
Externally publishedYes

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