{"docId":5509,"paperId":4813,"url":"https:\/\/dmtcs.episciences.org\/4813","doi":"10.23638\/DMTCS-21-1-5","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":341,"name":"vol. 21 no. 1, ICGT 2018"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"1808.08710","repositoryVersion":4,"repositoryLink":"https:\/\/arxiv.org\/abs\/1808.08710v4","dateSubmitted":"2018-09-10 11:22:06","dateAccepted":"2019-05-29 09:26:05","datePublished":"2019-05-29 09:26:16","titles":["Bisplit graphs satisfy the Chen-Chv\\'atal conjecture"],"authors":["Beaudou, Laurent","Kahn, Giacomo","Rosenfeld, Matthieu"],"abstracts":["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."],"keywords":["Computer Science - Discrete Mathematics","Mathematics - Combinatorics"]}