Vertex coverings by Monochromatic cycles and trees
Journal of Combinatorial Theory Series B
Multicolored forests in bipartite decompositions of graphs
Journal of Combinatorial Theory Series B
Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Partitioning by monochromatic trees
Journal of Combinatorial Theory Series B
Multicolored trees in complete graphs
Journal of Combinatorial Theory Series B
Partitioning complete bipartite graphs by monochromatic cycles
Journal of Combinatorial Theory Series B
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Generalized partitions of graphs
Discrete Applied Mathematics
Graph partition problems into cycles and paths
Discrete Mathematics
Graph colourings and partitions
Theoretical Computer Science
Partitioning into graphs with only small components
Journal of Combinatorial Theory Series B
Partitioning complete multipartite graphs by monochromatic trees
Journal of Graph Theory
Hi-index | 5.23 |
Let G=(V,E) be an edge-colored graph. A subgraph H is said to be monochromatic if all the edges of H have the same color, and multicolored if no two edges of H have the same color. We investigate the complexity of the problems for finding the minimum number of monochromatic or multicolored subgraphs, such as cliques, cycles, trees and paths, partitioning V(G), depending on the number of colors used and the maximal number of times a color appears in a coloring. We also present a greedy scheme that yields a (lnm+1)-approximation for the problem of finding the minimum number of monochromatic cliques partitioning V(G) for a K"4^--free graph G, where m is the size of the largest monochromatic clique in G. By a slightly modification of the approximation algorithm, it can be used for the multicolored case. We show that unless NP@?DTIME(N^O^(^l^o^g^l^o^g^N^)), for any @e=0 there is no approximation algorithm for finding the minimum number of multicolored trees partitioning V(G) with performance 50/521(1-@e)ln|V|.