The complexity of frugal colouring

Author:

Bard Stefan,MacGillivray GaryORCID,Redlin Shayla

Abstract

AbstractA t-frugal colouring of a graph G is an assignment of colours to the vertices of G, such that each colour appears at most t times in the neighbourhood of any vertex. A dichotomy theorem for the complexity of deciding whether a graph has a 1-frugal colouring with k colours was found by McCormick and Thomas, and then later extended to restricted graph classes by Kratochvil and Siggers. We generalize the McCormick and Thomas theorem by proving a dichotomy theorem for the complexity of deciding whether a graph has a t-frugal colouring with k colours, for all pairs of positive integers t and k. We also generalize bounds of Lih et al. for the number of colours needed in a 1-frugal colouring of a given $$K_4$$ K 4 -minor-free graph with maximum degree $$\Delta $$ Δ to t-frugal colourings, for any positive integer t.

Funder

Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference28 articles.

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