Geodesic
A note on removable edges in near-bricks
Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 2.

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An edge $e$ of a matching covered graph $G$ is removable if $G-e$ is also matching covered. Carvalho, Lucchesi, and Murty showed that every brick $G$ different from $K_4$ and $\overline{C_6}$ has at least $\Delta-2$ removable edges, where $\Delta$ is the maximum degree of $G$. In this paper, we generalize the result to irreducible near-bricks, where a graph is irreducible if it contains no single ear of length three or more.
DOI : 10.46298/dmtcs.11747
Classification : 05C70 
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Wu, Deyu; Zhang, Yipei; Wang, Xiumei. A note on removable edges in near-bricks. Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 2. doi : 10.46298/dmtcs.11747. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.11747/

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