This paper uncovers properties of claw-free bricks where all b-invariant edges are solitary, suggesting constraints on structure.
A graph G is a brick if it is 3-connected and G-,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, C₆̄ 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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Zhang et al. (2025) studied this question.
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