Communication: On the restricted homomorphism problem

Authors:
Richard C. Brewster;Timothy Graves
Affiliations:
Department of Mathematics and Statistics, Thompson Rivers University, PO Box 3010, Kamloops, BC, Canada, V2C 5N3;Department of Mathematics and Statistics, Thompson Rivers University, PO Box 3010, Kamloops, BC, Canada, V2C 5N3
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

The restricted homomorphism problemRHP(H,Y) asks: given an input digraph G and a homomorphism g:G-Y, does there exist a homomorphism f:G-H? We prove that if H is hereditarily hard and Y@?H, then RHP(H,Y) is NP-complete. Since non-bipartite graphs are hereditarily hard, this settles in the affirmative a conjecture of Hell and Nesetril.