Digraph matrix partitions and trigraph homomorphisms

Authors:
Tomás Feder;Pavol Hell;Kim Tucker-Nally
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, BC, Canada;School of Computing Science, Simon Fraser University, Burnaby, BC, Canada;Mathematics Department, Capilano College, North Vancouver, BC, Canada
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 19
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Abstract

Matrix partitions generalize graph colourings and homomorphisms. Their study has so far been confined to symmetric matrices and undirected graphs. In this paper we make an initial study of list matrix partitions for digraphs; in other words our matrices are not necessarily symmetric. We motivate future conjectures by classifying the complexity of all list matrix partition problems for matrices of size up to three. We find it convenient to model the problem in the language of trigraph homomorphisms.