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Preprint . 2023
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Discrete Mathematics
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Article . 2023
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Equitable coloring in 1-planar graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2025Embargo end date: 01 Jan 2023 English Publisher:Elsevier BVJournal:Discrete Mathematics, volume 348, page 114,286 (issn: 0012-365X, Copyright policy )
Authors: Daniel W. Cranston; Reem Mahmoud;

doi: 10.1016/j.disc.2024.114286 , 10.48550/arxiv.2311.14915

arXiv: 2311.14915

Equitable coloring in 1-planar graphs

Abstract

For every $r\ge13$, we show every 1-planar graph $G$ with $Δ(G)\le r$ has an equitable $r$-coloring.

9 figures

Related Organizations
Keywords

Coloring of graphs and hypergraphs, 05C15, equitable coloring conjecture, Hajnal-Szemerédi, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 1-planar, digraph, Planar graphs; geometric and topological aspects of graph theory

  • BIP!
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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 2
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green