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

TL;DR

This paper investigates $$-convexity on graphs, providing bounds and exact values for Helly and Radon numbers, and rank, especially for special classes like chordal and block graphs.

Contribution

It establishes general bounds and exact values for Helly, Radon numbers, and rank in $$-convexity on graphs, advancing understanding of convexity properties in graph theory.

Findings

Bounds for Helly, Radon numbers, and rank in $$-convexity.

Exact Helly and Radon numbers for chordal graphs.

Rank determination for block 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.