A ug 2 00 6 From Invariants to Canonization in Parallel
نویسنده
چکیده
A function f of a graph is called a complete graph invariant if G ∼= H is equivalent to f(G) = f(H). If, in addition, f(G) is a graph isomorphic to G, then f is called a canonical form for graphs. Gurevich [6] proves that graphs have a polynomial-time computable canonical form exactly when they have a polynomial-time computable complete invariant. We extend this equivalence to the polylogarithmic-time model of parallel computation for classes of graphs with bounded rigidity index and for classes of graphs with small separators. In particular, our results apply to 5-connected graphs of bounded genus and graphs with bounded treewidth. Since in the latter case an NC completeinvariant algorithm is known, we conclude that graphs of bounded treewidth have a canonical-labeling algorithm in NC.
منابع مشابه
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