English

Carath$\'{e}$odory Number and Exchange Number in $\Delta$-convexity

Combinatorics 2025-04-09 v2

Abstract

Given a graph GG, a set is Δ\Delta-convex if there is no vertex uV(G)Su\in V(G)\setminus S forming a triangle with two vertices of SS. The Δ\Delta-convex hull of SS is the minimum Δ\Delta-convex set containing SS. This article is an attempt to discuss the Carath\'eodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and, lexicographic products of graphs.

Keywords

Cite

@article{arxiv.2501.15025,
  title  = {Carath$\'{e}$odory Number and Exchange Number in $\Delta$-convexity},
  author = {Bijo S. Anand and Arun Anil and Manoj Changat and Prasanth G. Narasimha-Shenoi and Sabeer S. Ramla},
  journal= {arXiv preprint arXiv:2501.15025},
  year   = {2025}
}