Abstract
Motivated by the question of the relative complexities of the Graph Isomorphism and the Graph Automorphism problems, we define and study the modular graph automorphism problems. These are the decision problems ModkGA which consist, for each k > 1, of deciding whether the number of automorphisms of a graph is divisible by k. The ModkGA problems all turn out to be intermediate in difficulty between Graph Automorphism and Graph Isomorphism. We define an appropriate search version of ModkGA and design an algorithm that polynomial-time reduces the ModkGA search problem to the decision problem. Combining this algorithm with an IP protocol, we obtain a randomized polynomial-time checker for ModkGA, for all k > 1.
Supported in part by NSF grants CCR-8958528 and CCR-9415410, and NASA grant NAG 52895. Work done while on sabbatical from Yale University and affiliated with the Human-Computer Interaction Laboratory.
Supported in part by the E.U. through ESPRIT project (no. LTR 20244, ALCOMIT) and by DGICYT (Koala project, with no. PB95-0787), and CICYT (no. TIC971475-CE). Work completed while visiting the first author at the Institute of Mathematical Sciences.
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© 1998 Springer-Verlag
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Arvind, V., Beigel, R., Lozano, A. (1998). The complexity of modular graph automorphism. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028559
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DOI: https://doi.org/10.1007/BFb0028559
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