Extending cycles locally to Hamilton cycles

M. Hamann, Florian Lehner, Julian Pott

Research output: Contribution to journalArticlepeer-review

Abstract

A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle S1 that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs. Furthermore, we show that such graphs are Hamilton-connected if and only if they are 3-connected, extending a result of Asratian. Hamilton-connected means that between any two vertices there is a Hamilton arc, a homeomorphic copy of the unit interval [0,1] that contains all vertices and all ends precisely once.
Original languageEnglish
Article numberP1.49
Number of pages17
JournalThe Electronic Journal of Combinatorics
Volume23
Issue number1
DOIs
Publication statusPublished - 2016
Externally publishedYes

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