ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2019: 0.600
Rejection Rate (2018-2019): c. 84%
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
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,