A Polynomial Time Algorithm for Computing the Strong Rainbow Connection Numbers of Odd Cacti
share
We consider the problem of computing the strong rainbow connection number src(G) for cactus graphs G in which all cycles have odd length. We present a formula to calculate src(G) for such odd cacti which can be evaluated in linear time, as well as an algorithm for computing the corresponding optimal strong rainbow edge coloring, with polynomial worst case run time complexity. Although computing src(G) is NP-hard in general, previous work has demonstrated that it may be computed in polynomial time for certain classes of graphs, including cycles, trees and block clique graphs. This work extends the class of graphs for which src(G) may be computed in polynomial time.
READ FULL TEXT