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Some sufficient conditions for the existence of a 1-factor

✍ Scribed by Ladislav Nebeský

Publisher
John Wiley and Sons
Year
1978
Tongue
English
Weight
208 KB
Volume
2
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The following theorem is proved: Let G be a graph of even order. Assume that there exists a connected spanning subgraph F of G such that for every set U of four vertices in G, if the subgraph of F induced by U is a star, then the subgraph of G induced by U is complete. Then G has a 1‐factor. The above theorem is derived from another sufficient condition for the existence of a 1‐factor, which is also proved in this paper (Lemma 1).

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