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Even cycles and perfect matchings in claw-free plane graphs
2020
Discrete Mathematics & Theoretical Computer Science
Lov{\'a}sz showed that a matching covered graph $G$ has an ear decomposition starting with an arbitrary edge of $G$. Let $G$ be a graph which has a perfect matching. We call $G$ cycle-nice if for each even cycle $C$ of $G$, $G-V(C)$ has a perfect matching. If $G$ is a cycle-nice matching covered graph, then $G$ has ear decompositions starting with an arbitrary even cycle of $G$. In this paper, we characterize cycle-nice claw-free plane graphs. We show that the only cycle-nice simple 3-connected
doi:10.23638/dmtcs-22-4-6
fatcat:tfbq44jknbf5lg5i5oczyamzhm