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

2025/09/27 by Yipei Zhang, Xiumei Wang, Zhang, Yipei +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2509.23114

openalex publication_date 2025/09/27 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

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 K₄, C₆ 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.

Citations

• Cubic bricks that every b-invariant edge is forcing
• b-invariant edges in essentially 4-edge-connected near-bipartite cubic bricks
• On essentially 4-edge-connected cubic bricks

Related

• Solid bricks that every b-invariant edge is solitary
• Cubic bricks that every b-invariant edge is forcing
• b-invariant edges in essentially 4-edge-connected near-bipartite cubic bricks
• On a Norine–Thomas conjecture concerning minimal bricks
• Bricks and conjectures of Berge, Fulkerson and Seymour