Gutin, G., Majumdar, D., Ordyniak, S. orcid.org/0000-0003-1935-651X et al. (1 more author) (2020) Parameterized pre-coloring extension and list coloring problems. In: Paul, C. and Bläser, M., (eds.) Leibniz International Proceedings in Informatics, LIPIcs. 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020), 10-13 Mar 2020, Montpellier, France. Leibniz International Proceedings in Informatics (LIPIcs) (154). Schloss Dagstuhl - Leibniz-Zentrum für Informatik ISBN 9783959771405
Abstract
Golovach, Paulusma and Song (Inf. Comput. 2014) asked to determine the parameterized complexity of the following problems parameterized by k: (1) Given a graph G, a clique modulator D (a clique modulator is a set of vertices, whose removal results in a clique) of size k for G, and a list L(v) of colors for every v ∈ V(G), decide whether G has a proper list coloring; (2) Given a graph G, a clique modulator D of size k for G, and a pre-coloring λ_P: X → Q for X ⊆ V(G), decide whether λ_P can be extended to a proper coloring of G using only colors from Q. For Problem 1 we design an O*(2^k)-time randomized algorithm and for Problem 2 we obtain a kernel with at most 3k vertices. Banik et al. (IWOCA 2019) proved the following problem is fixed-parameter tractable and asked whether it admits a polynomial kernel: Given a graph G, an integer k, and a list L(v) of exactly n-k colors for every v ∈ V(G), decide whether there is a proper list coloring for G. We obtain a kernel with O(k²) vertices and colors and a compression to a variation of the problem with O(k) vertices and O(k²) colors.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. Licensed under Creative Commons License CC-BY (https://creativecommons.org/licenses/by/3.0/). |
Keywords: | Parameterized Algorithms; W-hardness; Kernelization; Graph Coloring; List Coloring |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 29 Apr 2020 09:05 |
Last Modified: | 29 Apr 2020 09:05 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Refereed: | Yes |
Identification Number: | 10.4230/LIPIcs.STACS.2020.19 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:160012 |