TY - GEN

T1 - On the rainbow connectivity of graphs

T2 - 17th Annual International Computing and Combinatorics Conference, COCOON 2011

AU - Uchizawa, Kei

AU - Aoki, Takanori

AU - Ito, Takehiro

AU - Suzuki, Akira

AU - Zhou, Xiao

PY - 2011/8/29

Y1 - 2011/8/29

N2 - For a graph G = (V,E) and a color set C, let f: E → C be an edge-coloring of G which is not necessarily proper. Then, the graph G edge-colored by f is rainbow connected if every two vertices of G has a path in which all edges are assigned distinct colors. Chakraborty et al. defined the problem of determining whether the graph colored by a given edge-coloring is rainbow connected. Chen et al. introduced the vertex-coloring version of the problem as a variant, and we introduce the total-coloring version in this paper. We settle the precise computational complexities of all the three problems from two viewpoints, namely, graph diameters and certain graph classes. We also give FPT algorithms for the three problems on general graphs when parameterized by the number of colors in C; these results imply that all the three problems can be solved in polynomial time for any graph with n vertices if |C| = O(logn).

AB - For a graph G = (V,E) and a color set C, let f: E → C be an edge-coloring of G which is not necessarily proper. Then, the graph G edge-colored by f is rainbow connected if every two vertices of G has a path in which all edges are assigned distinct colors. Chakraborty et al. defined the problem of determining whether the graph colored by a given edge-coloring is rainbow connected. Chen et al. introduced the vertex-coloring version of the problem as a variant, and we introduce the total-coloring version in this paper. We settle the precise computational complexities of all the three problems from two viewpoints, namely, graph diameters and certain graph classes. We also give FPT algorithms for the three problems on general graphs when parameterized by the number of colors in C; these results imply that all the three problems can be solved in polynomial time for any graph with n vertices if |C| = O(logn).

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U2 - 10.1007/978-3-642-22685-4_8

DO - 10.1007/978-3-642-22685-4_8

M3 - Conference contribution

AN - SCOPUS:80051962224

SN - 9783642226847

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 86

EP - 97

BT - Computing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings

Y2 - 14 August 2011 through 16 August 2011

ER -