4-Factor-Criticality of Vertex-Transitive Graphs
Keyword(s):
P Factor
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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 well-known factor-critical graphs and bicritical graphs, respectively. It is known that if a connected vertex-transitive graph has odd order, then it is factor-critical, otherwise it is elementary bipartite or bicritical. In this paper, we show that a connected vertex-transitive non-bipartite graph of even order at least 6 is 4-factor-critical if and only if its degree is at least 5. This result implies that each connected non-bipartite Cayley graph of even order and degree at least 5 is 2-extendable.
2009 ◽
Vol 3
(2)
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pp. 386-394
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2014 ◽
Vol 157
(1)
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pp. 45-61
2010 ◽
Vol 02
(02)
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pp. 151-160
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2019 ◽
Vol 11
(05)
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pp. 1930002
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2012 ◽
Vol 87
(3)
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pp. 441-447
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1994 ◽
Vol 56
(1)
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pp. 53-63
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