Bisplit graphs satisfy the Chen-Chv\'atal conjecture
Discrete Mathematics
2023-06-22 v4 Combinatorics
Abstract
In this paper, we give a lengthy proof of a small result! A graph is bisplit if its vertex set can be partitioned into three stable sets with two of them inducing a complete bipartite graph. We prove that these graphs satisfy the Chen-Chv\'atal conjecture: their metric space (in the usual sense) has a universal line (in an unusual sense) or at least as many lines as the number of vertices.
Cite
@article{arxiv.1808.08710,
title = {Bisplit graphs satisfy the Chen-Chv\'atal conjecture},
author = {Laurent Beaudou and Giacomo Kahn and Matthieu Rosenfeld},
journal= {arXiv preprint arXiv:1808.08710},
year = {2023}
}