Toughness and Matching Extension in Graphs,
VANDERBILT UNIV NASHVILLE TN DEPT OF MATHEMATICS
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In the present paper, we wish to treat some relationships between toughness of a graph and the n-extendability of the graph. We will prove two results. The first says essentially that if a graph has sufficiently high toughness and has an even number of points then it must be n-extendable. The second result applies to graphs with toughness less than one and presents an upper bound on the value of n for which such a graph can be n-extendable. In the final section, we compare and contrast these results with the n-factor results of Enomoto, Jackson, Katerinis and A. Saito.
- Numerical Mathematics