A new class of graphs that satisfies the Chen-Chv\'atal Conjecture
Combinatorics
2016-06-21 v1 Discrete Mathematics
Abstract
A well-known combinatorial theorem says that a set of n non-collinear points in the plane determines at least n distinct lines. Chen and Chv\'atal conjectured that this theorem extends to metric spaces, with an appropriated definition of line. In this work we prove a slightly stronger version of Chen and Chv\'atal conjecture for a family of graphs containing chordal graphs and distance-hereditary graphs.
Keywords
Cite
@article{arxiv.1606.06011,
title = {A new class of graphs that satisfies the Chen-Chv\'atal Conjecture},
author = {Pierre Aboulker and Martin Matamala and Paul Rochet and Jose Zamora},
journal= {arXiv preprint arXiv:1606.06011},
year = {2016}
}