论文信息 - Properties of Edge-Tough Graphs

Properties of Edge-Tough Graphs

Abstract. In [6] the author defined a new property of graphs namely the edge-toughness. It was proved in [6] that a 2t-tough graph is always t-edge-tough. It is proved in the present paper that this is not true for (2t−ε)-tough graphs if t is a positive integer. A result of Enomoto et al. in [5] implies that every 2-tough graph has a 2-factor. In the present paper it is proved that every 1-edge-tough graph has a 2-factor. This is a sharpening of the previous statement.

Gyula Y. Katona

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