Generalized rainbow connectivity of graphs

Kei Uchizawa, Takanori Aoki, Takehiro Ito, Gyo Shu

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

1 Citation (Scopus)

Abstract

Let C = {c1, c2, ..., ck} be a set of k colors, and let ℓ = (ℓ1, ℓ2, ..., ℓk) be a k-tuple of nonnegative integers ℓ1, ℓ2, ..., ℓk. For a graph G = (V,E), let f: E → C be an edge-coloring of G in which two adjacent edges may have the same color. Then, the graph G edge-colored by f is ℓ-rainbow connected if every two vertices of G have a path P such that the number of edges in P that are colored with cj is at most ℓj for each index j ∈{1,2,..., k}. Given a k-tuple ℓ and an edge-colored graph, we study the problem of determining whether the edge-colored graph is ℓ-rainbow connected. In this paper, we characterize the computational complexity of the problem with regards to certain graph classes: the problem is NP-complete even for cacti, while is solvable in polynomial time for trees. We then give an FPT algorithm for general graphs when parameterized by both k and ℓmax = max{ℓj

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings
Pages233-244
Number of pages12
DOIs
Publication statusPublished - 2013 Feb 4
Event7th International Workshop on Algorithms and Computation, WALCOM 2013 - Kharagpur, India
Duration: 2013 Feb 142013 Feb 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7748 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Workshop on Algorithms and Computation, WALCOM 2013
CountryIndia
CityKharagpur
Period13/2/1413/2/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Uchizawa, K., Aoki, T., Ito, T., & Shu, G. (2013). Generalized rainbow connectivity of graphs. In WALCOM: Algorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings (pp. 233-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7748 LNCS). https://doi.org/10.1007/978-3-642-36065-7_22