Equitable Colorings of $K_4$-minor-free Graphs

Rémi de Joannis de Verclos 1 Jean-Sébastien Sereni 2, 3
1 G-SCOP_OC - OC
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
3 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : We demonstrate that for every positive integer ∆, every K_4-minor-free graph with maximum degree ∆ admits an equitable coloring with k colors wherek ≥ (∆+3)/2. This bound is tight and confirms a conjecture by Zhang and Whu. We do not use the discharging method but rather exploit decomposition trees of K 4-minor-free graphs.
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https://hal.archives-ouvertes.fr/hal-01483972
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Submitted on : Monday, March 6, 2017 - 4:31:00 PM
Last modification on : Thursday, October 10, 2019 - 10:34:04 AM
Long-term archiving on : Wednesday, June 7, 2017 - 3:02:43 PM

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Rémi de Joannis de Verclos, Jean-Sébastien Sereni. Equitable Colorings of $K_4$-minor-free Graphs. Journal of Graph Algorithms and Applications, Brown University, 2017, 21 (6), pp.1091 - 1105. ⟨10.7155/jgaa.00451⟩. ⟨hal-01483972⟩

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