Hamilton cycles in infinite cubic graphs

2017/05/19 by Pitz, Max
#05C07 #05C45 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.07031

Abstract

Investigating a problem of B. Mohar, we show that every one-ended Hamiltonian cubic graph with end degree 3 contains a second Hamilton cycle. We also construct two examples showing that this result does not extend to give a third Hamilton cycle, nor that it extends to the two-ended case.

Related

• Hamiltonian cubic bipartite graphs
• On the Number of Cycles in a Graph
• Barnette's Conjecture
• Hamiltonian cycles in some family of cubic 3-connected plane graphs
• Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture