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A generalization of Petersen's theorem

✍ Scribed by Michel X. Goemans

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
338 KB
Volume
115
Category
Article
ISSN
0012-365X

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✦ Synopsis

Goemans, M.X., A generalization of Petersen's theorem, Discrete Mathematics 115 (1993) 277-282. Petersen's theorem asserts that any cubic graph with at most 2 cut edges has a perfect matching. We generalize this classical result by showing that any cubic graph G = (V, E) with at most 1 cut edge has a T-join of cardinality less than or equal to ( VI/2 for every even subset T of vertices. Our result is based on the Edmonds-Johnson min-max relation for T-joins.

In his 1891 landmark paper on the factorization of regular graphs, Petersen [6] (see Biggs et al. [l]) proved the following famous result.

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