Geodesic
Bisplit graphs satisfy the Chen-Chv\'atal conjecture
Discrete mathematics & theoretical computer science, ICGT 2018, Tome 21 (2019) no. 1.

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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. 
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     title = {Bisplit graphs satisfy the {Chen-Chv\'atal} conjecture},
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Beaudou, Laurent; Kahn, Giacomo; Rosenfeld, Matthieu. Bisplit graphs satisfy the Chen-Chv\'atal conjecture. Discrete mathematics & theoretical computer science, ICGT 2018, Tome 21 (2019) no. 1. doi : 10.23638/DMTCS-21-1-5. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-1-5/

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