On the rainbow connectivity of graphs: Complexity and FPT algorithms

Kei Uchizawa, Takanori Aoki, Takehiro Ito, Akira Suzuki, Xiao Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

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).

Original languageEnglish
Title of host publicationComputing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings
Pages86-97
Number of pages12
DOIs
Publication statusPublished - 2011 Aug 29
Event17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States
Duration: 2011 Aug 142011 Aug 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6842 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th Annual International Computing and Combinatorics Conference, COCOON 2011
CountryUnited States
CityDallas, TX
Period11/8/1411/8/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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