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Parameterized complexity of list coloring and Max coloring
, Article 17th International Computer Science Symposium in Russia, CSR 2022, 29 June 2022 through 1 July 2022 ; Volume 13296 LNCS , 2022 , Pages 46-63 ; 03029743 (ISSN); 9783031095733 (ISBN) ; Panolan, F ; Sharif University of Technology
Springer Science and Business Media Deutschland GmbH
2022
Abstract
In the List Coloring problem, the input is a graph G and list of colors L: V(G) → N for each vertex v∈ V(G). The objective is to test the existence of a coloring λ: V(G) → N such that for each v∈ V(G), λ(v) ∈ L(v) and for each edge (u, v) ∈ E(G), λ(u) ≠ λ(v). Fiala et al. (TCS 2011) proved that List Coloring is W[1]-hard when parameterized by the vertex cover number of the input graph. Recently, Gutin et al. (STACS 2020, SIDMA 2021) designed an O∗(2 k) time randomized algorithm for List Coloring where k is the size of the given clique modulator of the input graph. Since List Coloring is W[1]-hard parameterized by the vertex cover number, List Coloring is W[1]-hard parameterized by the size...