Helly Number, Radon Number and Rank in $\Delta$-Convexity on Graphs

Abstract

This article discusses $\Delta$-convexity on simple connected graphs. We establish general bounds for the Helly number, Radon number, and rank with respect to $\Delta$-convexity on graphs. Additionally, we give the exact values for the Helly number and Radon number for chordal graphs, as well as the rank for block graphs.

14 pages , 2 figures