### Abstract

Let C = {c_{1}, c_{2}, ..., c_{k}} be a set of k colors, and let ℓ = (ℓ_{1}, ℓ_{2}, ..., ℓ_{k}) be a k-tuple of nonnegative integers ℓ_{1}, ℓ_{2}, ..., ℓ_{k}. 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 c_{j} is at most ℓ_{j} 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 ℓ_{max} = max{ℓ_{j}

Original language | English |
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Title of host publication | WALCOM |

Subtitle of host publication | Algorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings |

Pages | 233-244 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2013 Feb 4 |

Event | 7th International Workshop on Algorithms and Computation, WALCOM 2013 - Kharagpur, India Duration: 2013 Feb 14 → 2013 Feb 16 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7748 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th International Workshop on Algorithms and Computation, WALCOM 2013 |
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Country | India |

City | Kharagpur |

Period | 13/2/14 → 13/2/16 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*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