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arXiv · 1611.09531

Three matching intersection property for matching covered graphs

Hao Lin·Xiumei Wang
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Abstract

In connection with Fulkerson's conjecture on cycle covers, Fan and Raspaud proposed a weaker conjecture: For every bridgeless cubic graph $G$, there are three perfect matchings $M_1$, $M_2$, and $M_3$ such that $M_1\cap M_2 \cap M_3=\emptyset$. We call the property specified in this conjecture the three matching intersection property (and 3PM property for short). We study this property on matching covered graphs. The main results are a necessary and sufficient condition and its applications to characterization of special graphs, such as the Halin graphs and 4-regular graphs.

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Hao Lin, Xiumei Wang. 2016-11-29. Three matching intersection property for matching covered graphs. https://doi.org/10.23638/dmtcs-19-3-16

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