On Reachability in Graphs with Bounded Independence Number

Authors:
Arfst Nickelsen;Till Tantau
Affiliations:
-;-
Venue:
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Year:
2002

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Abstract

We study the reachability problem for finite directed graphs whose independence number is bounded by some constant k. This problem is a generalisation of the reachability problem for tournaments. We show that the problem is first-order definable for all k. In contrast, the reachability problems for many other types of finite graphs, including dags and trees, are not first-order definable. Also in contrast, first-order definability does not carry over to the infinite version of the problem. We prove that the number of strongly connected components in a graph with bounded independence number can be computed using TC0-circuits, but cannot be computed using AC0-circuits. We also study the succinct version of the problem and show that it is 驴P2 -complete for all k.