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arXiv · 2308.09491

A note on removable edges in near-bricks

Deyu Wu·Yipei Zhang·Xiumei Wang
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Abstract

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 $Δ-2$ removable edges, where $Δ$ 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.

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Deyu Wu, Yipei Zhang, Xiumei Wang. 2024-06-18. A note on removable edges in near-bricks. https://doi.org/10.46298/dmtcs.11747

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