On the total chromatic number of the direct product of cycles and complete graphs

• Published in: R.A.I.R.O. Recherche opérationnelle Vol. 58; no. 2; pp. 1609 - 1632
• Main Authors: Castonguay, Diane, de Figueiredo, Celina M.H., Kowada, Luis A.B., Patrão, Caroline S.R., Sasaki, Diana, Valencia-Pabon, Mario
• Format: Journal Article
• Language: English
• Published: Paris EDP Sciences 01.03.2024
• Subjects: Apexes; Color; Coloring; Graph theory

A k-total coloring of a graph G is an assignment of k colors to the elements (vertices and edges) of G so that adjacent or incident elements have different colors. The total chromatic number is the smallest integer k for which G has a k -total coloring. The well known Total Coloring Conjecture state...