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On the 2-factors of bicubic graphs

✍ Scribed by W.T. Tutte

Publisher: Elsevier Science
Year: 1971
Tongue: English
Weight: 291 KB
Volume: 1
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(71)90027-6

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✦ Synopsis

A cubt~ g~aph of 2n vet "th:es and Po components has n + PO linearly independent 2-fact(~ Thus each cycle of the graph can b: expressed as a rood 2 sum of 2-factogs. Only fini~ f~phs are conside~d.

The number of vertices of a trivalent graph must be even. If we write it as ~ then the number of edges is 3n. We define a bicubic graph as it bipar¢ite trivalent graph. It is easy to prove that a bicubic graph has no isthmus and no loop.

An n-factor of a ~'aph G, where n is a positive integer, is a set of

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