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 language | English |
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Article number | P1.49 |
Number of pages | 17 |
Journal | The Electronic Journal of Combinatorics |
Volume | 23 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2016 |
Externally published | Yes |