Fixed-Parameter tractability of (n-k) list coloring

Aritra Banik, Ashwin Jacob, Vijay Kumar Paliwal, Venkatesh Raman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


We consider the list-coloring problem from the perspective of parameterized complexity. The classical graph coloring problem is given an undirected graph and the goal is to color the vertices of the graph with minimum number of colors so that end points of each edge gets different colors. In list-coloring, each vertex is given a list of allowed colors with which it can be colored. In parameterized complexity, the goal is to identify natural parameters in the input that are likely to be small and design an algorithm with time f(k)nc time where c is a constant independent of k, and k is the parameter. Such an algorithm is called a fixed-parameter tractable (fpt) algorithm. It is clear that the solution size as a parameter is not interesting for graph coloring, as the problem is NP-hard even for k=3. An interesting parameterization for graph coloring that has been studied is whether the graph can be colored with n-k colors, where k is the parameter and n is the number of vertices. This is known to be fpt using the notion of crown reduction. Our main result is that this can be generalized for list-coloring as well. More specifically, we show that, given a graph with each vertex having a list of size n-k, it can be determined in f(k)nO(1) time, for some function f of k, whether there is a coloring that respects the lists.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings
EditorsCharles J. Colbourn, Roberto Grossi, Nadia Pisanti
PublisherSpringer Verlag
Number of pages9
ISBN (Print)9783030250041
StatePublished - 1 Jan 2019
Externally publishedYes
Event30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, Italy
Duration: 23 Jul 201925 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11638 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference30th International Workshop on Combinatorial Algorithms, IWOCA 2019

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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