ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

Article in press


K. Giaro and M. Kubale


A note on polynomial algorithm for cost coloring of bipartite graphs with $\Delta\leq 4$


Discussiones Mathematicae Graph Theory

Received: 2018-10-18, Accepted: 2019-03-19,


In the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for $n$-vertex bipartite graph of degree $\Delta \leq 4$ can be solved in O$(n^2)$ time. This extends Jansen's result [K. Jansen, The optimum cost chromatic partition problem, in: Proc. CIAC'97, Lecture Notes in Comput. Sci. 1203 (1997) 25–36] for paths and cycles to subgraphs of biquartic graphs.


bipartite graph, chromatic sum, cost coloring, NP-completeness, polynomial algorithm