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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Graphs with $1$-factors
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by David P. Sumner PDF
Proc. Amer. Math. Soc. 42 (1974), 8-12 Request permission

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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 42 (1974), 8-12
  • MSC: Primary 05C99
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0323648-6
  • MathSciNet review: 0323648