Work

Hadwiger’s Conjecture for Dense Strongly Regular Graphs

Year: 2025

Type: article

Abstract: The famous Four-Color Conjecture (now Theorem) states that any planar graph could be colored using four colors. Hadwiger’s conjecture strengthens the Four-Color Conjecture by asserting that every graph with chromatic number t contains a complete minor of order t. In this paper we investigate Hadwiger’s conjecture for the complements of the Petersen graph and the Clebsch graph; both are strongly regular graphs with independence number two (hence dense graphs). We confirm Hajós’ conjecture, hence Hadwiger’s conjecture, for these graphs. Moreover, we show that for each of these graphs the exact hadwiger number is strictly greater its chromatic number.

Source: Symmetry

DOI: 10.3390/sym17101588

Authors: Guangjun Xu, Lijuan Lei, Xianghu Liu, Yanfang Li

Institutions: Suqian University, Henan Agricultural University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funders: National Natural Science Foundation of China, Guizhou Science and Technology Department