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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Graphs with $ 1$-factors


Author: David P. Sumner
Journal: Proc. Amer. Math. Soc. 42 (1974), 8-12
MSC: Primary 05C99
MathSciNet review: 0323648
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Abstract: In this paper it is shown that if G is a connected graph of order $ 2n(n > 1)$ not containing a 1-factor, then for each k, $ 1 < k \leqq n$, there exists an induced; connected subgraph of order 2k which also fails to possess a 1-factor. Several other sufficient conditions for a graph to contain a 1-factor are presented. In particular, it is seen that the connected even order line graphs and total graphs always contain a 1-factor.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0323648-6
PII: S 0002-9939(1974)0323648-6
Article copyright: © Copyright 1974 American Mathematical Society