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STACS
2009
Springer

Hardness and Algorithms for Rainbow Connectivity

13 years 10 months ago
Hardness and Algorithms for Rainbow Connectivity
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In addition to being a natural combinatorial problem, the rainbow connectivity problem is motivated by applications in cellular networks. In this paper we give the first proof that computing rc(G) is NP-Hard. In fact, we prove that it is already NP-Complete to decide if rc(G) = 2, and also that it is NP-Complete to decide whether a given edge-colored (with an unbounded number of colors) graph is rainbow connected. On the positive side, we prove that for every ǫ > 0, a connected graph with minimum degree at least ǫn has bounded rainbow connectivity, where the bound depends only on ǫ, and the corresponding coloring can be constructed in polynomial time. Additional non-trivial upper bounds, as well as open proble...
Sourav Chakraborty, Eldar Fischer, Arie Matsliah,
Added 20 May 2010
Updated 20 May 2010
Type Conference
Year 2009
Where STACS
Authors Sourav Chakraborty, Eldar Fischer, Arie Matsliah, Raphael Yuster
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