Geodesic
Three matching intersection property for matching covered graphs
Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3.

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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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     author = {Lin, Hao and Wang, Xiumei},
     title = {Three matching intersection property for matching covered graphs},
     journal = {Discrete mathematics & theoretical computer science},
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Lin, Hao; Wang, Xiumei. Three matching intersection property for matching covered graphs. Discrete mathematics & theoretical computer science, Tome 19 (2017-2018) no. 3. doi : 10.23638/DMTCS-19-3-16. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-3-16/

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