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List homomorphisms of graphs with bounded degrees. (English) Zbl 1111.05035

Summary: In a series of papers, we have classified the complexity of list homomorphism problems. Here, we investigate the effect of restricting the degrees of the input graphs. It turns out that the complexity does not change (except when the degree bound is two). We obtain similar results on restricting the size of the lists. We contrast these results with facts about variants of the list homomorphism problem, where restricting the degrees can have an important effect on the complexity.

MSC:

05C15 Coloring of graphs and hypergraphs
05C85 Graph algorithms (graph-theoretic aspects)
68R10 Graph theory (including graph drawing) in computer science
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