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Carathéodory Number and Exchange Number in Δ-convexity

2025/01/25 by Bijo S. Anand, Anand, Bijo S., Arun Anil +7
Mathematics · Computer Science · #Point processes and geometric inequalities #Optimization and Variational Analysis #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2501.15025

Abstract

Given a graph G, a set is Δ-convex if there is no vertex u∈ V(G)∖ S forming a triangle with two vertices of S. The Δ-convex hull of S is the minimum Δ-convex set containing S. This article is an attempt to discuss the Carathéodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and, lexicographic products of graphs.

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