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Graphs with 1-Factors

David P. Sumner
Proceedings of the American Mathematical Society
Vol. 42, No. 1 (Jan., 1974), pp. 8-12
DOI: 10.2307/2039666
Stable URL: http://www.jstor.org/stable/2039666
Page Count: 5
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Graphs with 1-Factors
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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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