The complexity of parity graph homomorphism: an initial investigation

John Faben; Mark Jerrum

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arXiv · 1309.4033

The complexity of parity graph homomorphism: an initial investigation

John Faben·Mark Jerrum

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Abstract

Given a graph G, we investigate the question of determining the parity of the number of homomorphisms from G to some other fixed graph H. We conjecture that this problem exhibits a complexity dichotomy, such that all parity graph homomorphism problems are either polynomial-time solvable or parityP-complete, and provide a conjectured characterisation of the easy cases. We show that the conjecture is true for the restricted case in which the graph H is a tree, and provide some tools that may be useful in further investigation into the parity graph homomorphism problem, and the problem of counting homomorphisms for other moduli.

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John Faben, Mark Jerrum. 2013-09-16. The complexity of parity graph homomorphism: an initial investigation. https://arxiv.org/abs/1309.4033

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