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

Yipei Zhang; Xiumei Wang

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

Combinatorics 2025-09-30 v1

Authors: Yipei Zhang , Xiumei Wang

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.

Keywords

brick b-invariant edge solitary edge claw-free graph perfect matching characterization

Cite

@article{arxiv.2509.23114,
  title  = {Claw-free bricks that every $b$-invariant edge is solitary},
  author = {Yipei Zhang and Xiumei Wang},
  journal= {arXiv preprint arXiv:2509.23114},
  year   = {2025}
}

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