Total-colorings of complete multipartite graphs using amalgamations

• Published in: Discrete mathematics Vol. 339; no. 5; pp. 1587 - 1592
• Main Authors: Dalal, Aseem, Panda, B.S., Rodger, C.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 06.05.2016
• Subjects: Amalgamation; Graph amalgamation; Graph theory; Graphs; Mathematical analysis; Multipartite graph; Settling; Total coloring; Total coloring; Multipartite graph; Graph amalgamation

This paper makes progress towards settling the long-standing conjecture that the total chromatic number χ″ of the complete p-partite graph K=K(r1,…,rp) is Δ(K)+1 if and only if K≠Kr,r and if K has an even number of vertices then Σv∈V(K)(Δ(K)−dK(v)) is at least the number of parts of odd size. Graphs...