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-Chvátal 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.

Source : oai:arXiv.org:1808.08710

Volume: vol. 21 no. 1, ICGT 2018

Published on: May 29, 2019

Submitted on: September 10, 2018

Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics