Disconnected 2-factors in planar cubic bridgeless graphs

Authors:
Ajit A. Diwan
Affiliations:
Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, Mumbai, India
Venue:
Journal of Combinatorial Theory Series B
Year:
2002

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Abstract

We prove that every planar cubic bridgeless graph with at least six vertices has a disconnected 2-factor, that is a 2-factor which is not a Hamilton cycle. This is in contrast to the fact that there exist arbitrarily large cubic bridgeless graphs in which every 2-factor is a Hamilton cycle.