Paper Info
Title
Rainbow Connectivity: Hardness and Tractability.
Abstract
A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. In this paper we study the rainbow connectivity problem and the strong rainbow connectivity problem from a computational point of view. Our main results can be summarised as below: For every fixed k >= 3, it is NP-Complete to decide whether src(G) <= k even when the graph G is bipartite. For every fixed odd k >= 3, it is NP-Complete to decide whether rc(G) <= k. This resolves one of the open problems posed by Chakraborty et al. [4] hardness for the even case. The following problem is fixed parameter tractable: Given a graph G, determine the maximum number of pairs of vertices that can be rainbow connected using two colors. For a directed graph G, it is NP-Complete to decide whether rc(G) <= 2.
Year
DOI
Venue
2011
10.4230/LIPIcs.FSTTCS.2011.241
Leibniz International Proceedings in Informatics
Keywords
Field
DocType
Computational Complexity,Rainbow Connectivity,Graph Theory,Fixed Parameter Tractable Algorithms
Discrete mathematics,Edge coloring,Graph toughness,Combinatorics,Bound graph,Graph power,Cycle graph,Connectivity,Mathematics,Complement graph,Path graph
Conference
Volume
ISSN
Citations 
13
1868-8969
12
PageRank 
References 
Authors
0.79
6
3
Name
Order
Citations
PageRank
Prabhanjan Ananth123418.43
Meghana Nasre29812.80
Kanthi K. Sarpatwar3308.03