Equitable colorings of corona multiproducts of graphs
Hanna Furmańczyk , Marek Kubale , Vahan V. Mkrtchyan
AbstractA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by χ=(G). It is known that the problem of computation of χ=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013) 103–120].
|Other language title versions|
|Journal series||Discussiones Mathematicae Graph Theory, ISSN 1234-3099, (A 15 pkt)|
|Publication size in sheets||0.75|
|Keywords in English||Corona graph, equitable chromatic number, equitable coloring conjecture, equitable graph coloring, multiproduct of graphs, NP-completeness, polynomial algorithm|
|License||Journal (articles only); published final; ; with publication|
|Score|| = 15.0, ArticleFromJournal|
= 15.0, ArticleFromJournal
|Publication indicators||: 2017 = 0.601 (2) - 2017=0.535 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.