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Bounded color multiplicity graph isomorphism is in the #L hierarchy

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3 Author(s)
Arvind, V. ; Inst. of Math. Sci., C.I.T Campus, Chennai, India ; Kurur, P.P. ; Vijayaraghavan, T.C.

In this paper we study the complexity of bounded color multiplicity graph isomorphism BCGIb: the input is a pair of vertex-colored graphs such that the number of vertices of a given color in an input graph is bounded by b. We show that BCGIb is in the #L hierarchy (more precisely, the ModkL hierarchy for some constant k depending on b). Combined with the fact that bounded color multiplicity graph isomorphism is logspace many-one hard for every set in the ModkL hierarchy for any constant k, we get a tight classification of the problem using logspace-bounded counting classes.

Published in:

Computational Complexity, 2005. Proceedings. Twentieth Annual IEEE Conference on

Date of Conference:

11-15 June 2005