Reachability In K3,3-free graphs and K5-free graphs is in unambiguous log-space
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
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For several problems, restricting attention to special classes of graphs has yielded better algorithms. In particular, restricting to planar graphs yields efficient parallel algorithms for several graph problems. In this paper, we extend these algorithms to $K_{5}$-minor free graphs, showing that the restriction of planarity is not important. The two problems dealt with are: graph coloring and maximal independent sets. We also show that $K_{5}$-minor free graphs are four colorable (this bound is tight). We also give an NC algorithms to recognize $K_{5}$-minor free graphs.