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arXiv · 1212.3940

3-Factor-criticality of vertex-transitive graphs

Heping Zhang·Wuyang Sun
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Abstract

A graph of order $n$ is $p$-factor-critical, where $p$ is an integer of the same parity as $n$, if the removal of any set of $p$ vertices results in a graph with a perfect matching. 1-Factor-critical graphs and 2-factor-critical graphs are factor-critical graphs and bicritical graphs, respectively. It is well known that every connected vertex-transitive graph of odd order is factor-critical and every connected non-bipartite vertex-transitive graph of even order is bicritical. In this paper, we show that a simple connected vertex-transitive graph of odd order at least 5 is 3-factor-critical if and only if it is not a cycle.

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Heping Zhang, Wuyang Sun. 2012-12-17. 3-Factor-criticality of vertex-transitive graphs. https://arxiv.org/abs/1212.3940

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