We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP-complete on planar bipartite graphs with Δ ≤ 5, but polynomial on bipartite graphs with Δ ≤ 3, for which we construct an O(n2)-time algorithm. Hence, we tighten the borderline of intractability for this problem on bipartite graphs with bounded degree, namely: the case Δ = 3 is easy, Δ = 5 is hard. Moreover, we construct a 27/26-approximation algorithm for this problem thus improving the best known approximation ratio of 10/9.
CITATION STYLE
Giaro, K., Janczewski, R., Kubale, M., & Maƚafiejski, M. (2002). A 27/26-approximation algorithm for the chromatic sum coloring of bipartite graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2462, pp. 135–145). Springer Verlag. https://doi.org/10.1007/3-540-45753-4_13
Mendeley helps you to discover research relevant for your work.