2016/06/20 by Aboulker, Pierre, Matamala, Martin, Rochet, Paul +1 · 2 citations
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1606.06011
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 Chvátal 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 Chvátal conjecture for a family of graphs containing chordal graphs and distance-hereditary graphs.