Title:
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Fast recoloring of sparse graphs
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Author:
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Bousquet, Nicolas; Perarnau Llobet, Guillem
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
Abstract:
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This is a post-peer-review, pre-copyedit version of an article published in European Journal of Combinatorics. The final authenticated version is available online at: https://doi.org/10.1016/j.ejc.2015.08.001 |
Abstract:
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In this paper, we show that for every graph of maximum average degree bounded away from d and any two (d + 1)-colorings of it, one can transform one coloring into the other one within a polynomial number of vertex recolorings so that, at each step, the current coloring is proper. In particular, it implies that we can transform any 8-coloring of a planar graph into any other 8-coloring with a polynomial number of recolorings. These results give some evidence on a conjecture of Cereceda et al [8] which asserts that any (d + 2) coloring of a d-degenerate graph can be transformed into any other one using a polynomial number of recolorings. We also show that any (2d + 2)-coloring of a d-degenerate graph can be transformed into any other one with a linear number of recolorings. |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Graph theory -Grafs, Teoria de |
Rights:
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Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Document type:
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Article - Submitted version Article |
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