TY - GEN

T1 - Generalized rainbow connectivity of graphs

AU - Uchizawa, Kei

AU - Aoki, Takanori

AU - Ito, Takehiro

AU - Zhou, Xiao

PY - 2013

Y1 - 2013

N2 - 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 | 1 ≤ j ≤ k}.

AB - 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 | 1 ≤ j ≤ k}.

UR - http://www.scopus.com/inward/record.url?scp=84873847852&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873847852&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36065-7_22

DO - 10.1007/978-3-642-36065-7_22

M3 - Conference contribution

AN - SCOPUS:84873847852

SN - 9783642360640

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

SP - 233

EP - 244

BT - WALCOM

T2 - 7th International Workshop on Algorithms and Computation, WALCOM 2013

Y2 - 14 February 2013 through 16 February 2013

ER -