Note: The Ck-extended graft construction

Authors:
Gary MacGillivray;Jacobus Swarts
Affiliations:
Mathematics and Statistics, University of Victoria, PO BOX 3060 STN CSC, Victoria, B.C., Canada V8W 3R4;Department of Mathematics, Vancouver Island University, 900 Fifth Street, Nanaimo, B.C., Canada V9R 5S5
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Gutjahr, Welzl and Woeginger found polynomial-time algorithms for a number of digraph homomorphism problems. These algorithms are based on the X@?-enumeration, theC"k-extended X@?-enumeration and the X@?-graft construction. In this note, we show how the last two methods can be combined to obtain new polynomial-time algorithms, which also work for list homomorphisms. In the process, we are able to extend results of Bang-Jensen and Hell, dealing with homomorphisms to bipartite tournaments, to list homomorphisms.