License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ISAAC.2020.58
URN: urn:nbn:de:0030-drops-134027
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Chen, Hubie ; Jansen, Bart M. P. ; Okrasa, Karolina ; Pieterse, Astrid ; Rzążewski, Paweł

Sparsification Lower Bounds for List H-Coloring

LIPIcs-ISAAC-2020-58.pdf (0.8 MB)


We investigate the List H-Coloring problem, the generalization of graph coloring that asks whether an input graph G admits a homomorphism to the undirected graph H (possibly with loops), such that each vertex v ∈ V(G) is mapped to a vertex on its list L(v) ⊆ V(H). An important result by Feder, Hell, and Huang [JGT 2003] states that List H-Coloring is polynomial-time solvable if H is a so-called bi-arc graph, and NP-complete otherwise. We investigate the NP-complete cases of the problem from the perspective of polynomial-time sparsification: can an n-vertex instance be efficiently reduced to an equivalent instance of bitsize 𝒪(n^(2-ε)) for some ε > 0? We prove that if H is not a bi-arc graph, then List H-Coloring does not admit such a sparsification algorithm unless NP ⊆ coNP/poly. Our proofs combine techniques from kernelization lower bounds with a study of the structure of graphs H which are not bi-arc graphs.

BibTeX - Entry

  author =	{Hubie Chen and Bart M. P. Jansen and Karolina Okrasa and Astrid Pieterse and Pawe{\l} Rzążewski},
  title =	{{Sparsification Lower Bounds for List H-Coloring}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{58:1--58:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-134027},
  doi =		{10.4230/LIPIcs.ISAAC.2020.58},
  annote =	{Keywords: List H-Coloring, Sparsification, Constraint Satisfaction Problem}

Keywords: List H-Coloring, Sparsification, Constraint Satisfaction Problem
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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