Connected Coloring Completion for General Graphs: Algorithms and Complexity

An r-component connected coloring of a graph is a coloring of the vertices so that each color class induces a subgraph having at most r connected components. The concept has been well-studied for r = 1, in the case of trees, under the rubric of convex coloring, used in modeling perfect phylogenies. Several applications in bioinformatics of connected coloring problems on general graphs are discussed, including analysis of protein-protein interaction networks and protein structure graphs, and of phylogenetic relationships modeled by splits trees. We investigate the r-COMPONENT CONNECTED COLORING COMPLETION (r-CCC) problem, that takes as input a partially colored graph, having k uncolored vertices, and asks whether the partial coloring can be completed to an r-component connected coloring. For r = 1 this problem is shown to be NPhard, but fixed-parameter tractable when parameterized by the number of uncolored vertices, solvable in time O∗ (8k ). We also show that the 1-CCC problem, par...

• Type: Conference
• Year: 2007
• Where: COCOON
• Authors: Benny Chor, Michael R. Fellows, Mark A. Ragan, Igor Razgon, Frances A. Rosamond, Sagi Snir
• Keywords: COCOON 2007, Connected Coloring, Connected Coloring Problems, R-component Connected Coloring