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arXiv · 2509.23114

Claw-free bricks that every $b$-invariant edge is solitary

Yipei Zhang·Xiumei Wang
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Abstract

A graph $G$ is a brick if it is 3-connected and $G-\{u,v\}$ has a perfect matching for any two distinct vertices $u$ and $v$ of $G$. Lucchesi and Murty proposed a problem concerning the characterization of bricks, distinct from $K_4$, $\overline{C_6}$ and the Petersen graph, in which every $b$-invariant edge is solitary. In this paper, we present a characterization of this problem when the bricks are claw-free.

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Yipei Zhang, Xiumei Wang. 2025-09-27. Claw-free bricks that every $b$-invariant edge is solitary. https://arxiv.org/abs/2509.23114

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