A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle $S^1$ 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.
@article{10_37236_3960,
author = {Matthias Hamann and Florian Lehner and Julian Pott},
title = {Extending cycles locally to {Hamilton} cycles},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {1},
doi = {10.37236/3960},
zbl = {1335.05122},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3960/}
}
TY - JOUR
AU - Matthias Hamann
AU - Florian Lehner
AU - Julian Pott
TI - Extending cycles locally to Hamilton cycles
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3960/
DO - 10.37236/3960
ID - 10_37236_3960
ER -
%0 Journal Article
%A Matthias Hamann
%A Florian Lehner
%A Julian Pott
%T Extending cycles locally to Hamilton cycles
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3960/
%R 10.37236/3960
%F 10_37236_3960
Matthias Hamann; Florian Lehner; Julian Pott. Extending cycles locally to Hamilton cycles. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/3960
