Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Bok, Jan; Brewster, Richard; Feder, Tomás; Hell, Pavol; Jedličková, Nikola License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-126886

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List Homomorphism Problems for Signed Graphs



We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph (G,σ), equipped with lists L(v) ⊆ V(H), v ∈ V(G), of allowed images, to a fixed target signed graph (H,π). The complexity of the similar homomorphism problem without lists (corresponding to all lists being L(v) = V(H)) has been previously classified by Brewster and Siggers, but the list version remains open and appears difficult. Both versions (with lists or without lists) can be formulated as constraint satisfaction problems, and hence enjoy the algebraic dichotomy classification recently verified by Bulatov and Zhuk. By contrast, we seek a combinatorial classification for the list version, akin to the combinatorial classification for the version without lists completed by Brewster and Siggers. We illustrate the possible complications by classifying the complexity of the list homomorphism problem when H is a (reflexive or irreflexive) signed tree. It turns out that the problems are polynomial-time solvable for certain caterpillar-like trees, and are NP-complete otherwise. The tools we develop will be useful for classifications of other classes of signed graphs, and we mention some follow-up research of this kind; those classifications are surprisingly complex.

BibTeX - Entry

  author =	{Jan Bok and Richard Brewster and Tom{\'a}s Feder and Pavol Hell and Nikola Jedličkov{\'a}},
  title =	{{List Homomorphism Problems for Signed Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-126886},
  doi =		{10.4230/LIPIcs.MFCS.2020.20},
  annote =	{Keywords: complexity, dichotomy, graph homomorphism, signed graph}

Keywords: complexity, dichotomy, graph homomorphism, signed graph
Seminar: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue date: 2020
Date of publication: 18.08.2020

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