Abstract.
A graph is (r,k)-factor-critical if the removal of any set of k vertices results in a graph with an r-factor (i.e. an r-regular spanning subgraph). Let t(G) denote the toughness of graph G. In this paper, we show that if t(G)≥4, then G is (3,k)-factor-critical for every non-negative integer k such that n+k even, k<2 t(G)−2 and k≤n−7.
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Revised: September 21, 1998
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Shi, M., Yuan, X., Cai, Mc. et al. (3,k)-Factor-Critical Graphs and Toughness. Graphs Comb 15, 463–471 (1999). https://doi.org/10.1007/s003730050053
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DOI: https://doi.org/10.1007/s003730050053