A characterization of graphs of diameter two with fewer lines than vertices
Abstract
In 2008 Chen and Chv\'atal conjectured that any metric space on n points has at least n lines, unless all the points belong to one line. Chv proved in 2014 that this is indeed the case for metric spaces with distances 0, 1 and 2. In this work, we prove that there exists a family of ten graphs such that a metric space defined by a graph of diameter two has fewer lines than points if and only if the associated graph belongs to that family.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.