List Homomorphisms to Reflexive Graphs

@article{Feder1998ListHT,
  title={List Homomorphisms to Reflexive Graphs},
  author={Tom{\'a}s Feder and Pavol Hell},
  journal={J. Comb. Theory, Ser. B},
  year={1998},
  volume={72},
  pages={236-250}
}
  • T. Feder, P. Hell
  • Published 1 March 1998
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
LetHbe a fixed graph. We introduce the following list homomorphism problem: Given an input graphGand for each vertexvofGa “list”L(v)?V(H), decide whether or not there is a homomorphismf:G?Hsuch thatf(v)?L(v) for eachv?V(G). We discuss this problem primarily in the context of reflexive graphs, i.e., graphs in which each vertex has a loop. We give a polynomial time algorithm to solve the problem whenHis an interval graph and prove that whenHis not an interval graph the problem isNP-complete. If… Expand
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It is shown that the list homomorphism problem is polynomial time solvable if the complement of H is a circular arc graph of clique covering number two, and is NP-complete otherwise. Expand
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Let H be a fixed digraph. We consider the H-colouring problem, i.e., the problem of deciding which digraphs G admit a homomorphism to H. We are interested in a characterization in terms of theExpand
List Homomorphisms to Reflexive Graphs
LetHbe a fixed graph. We introduce the following list homomorphism problem: Given an input graphGand for each vertexvofGa “list”L(v) V(H), decide whether or not there is a homomorphismf:G Hsuch tha...
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