Lengths of cycles in halin graphs

J. A. Bondy, L. Lovász

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

A Halin graph is a plane graph H = T U C, where T is a plane tree with no vertex of degree two and at least one vertex of degree three or more, and C is a cycle connecting the endvertices of T in the cyclic order determined by the embedding of T. We prove that such a graph on n vertices contains cycles of all lengths l, 3 ≤ l n, except, possibly, for one even value m of l. We prove also that if the tree T contains no vertex of degree three then G is pancyclic.

Original languageEnglish
Pages (from-to)397-410
Number of pages14
JournalJournal of Graph Theory
Volume9
Issue number3
DOIs
Publication statusPublished - 1985

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ASJC Scopus subject areas

  • Geometry and Topology

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