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Extending edge-colorings of distance-2 matchings in the hypercube.

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Title: Extending edge-colorings of distance-2 matchings in the hypercube.
Authors: Bärnkopf, Pál1 (AUTHOR) barpal@student.elte.hu
Source: Discrete Applied Mathematics. Jul2026, Vol. 387, p33-36. 4p.
Subjects: Hypercubes, Graph coloring, Bipartite graphs, Graph theory, Matching theory
Abstract: Casselgren, Markstörm, and Pham conjectured that any precolored distance-2 matching in the d -dimensional cube Q d with at most d colors can be extended to a proper d -edge-coloring. In this paper, we prove this conjecture and some related theorems. Especially, our result establishes that if G is a bipartite graph, then a precolored distance-2 matching in the Cartesian product H = G □ K 2 m with at most χ ′ (H) = Δ (H) = Δ (G) + 2 m − 1 colors can be extended to an edge-coloring using at most χ ′ (H) colors. As another generalization, we establish a similar result for the Cartesian product G □ K 1 , m . [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193089968
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  Data: Extending edge-colorings of distance-2 matchings in the hypercube.
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  Data: <searchLink fieldCode="AR" term="%22Bärnkopf%2C+Pál%22">Bärnkopf, Pál</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> barpal@student.elte.hu</i>
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jul2026, Vol. 387, p33-36. 4p.
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  Data: <searchLink fieldCode="DE" term="%22Hypercubes%22">Hypercubes</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+coloring%22">Graph coloring</searchLink><br /><searchLink fieldCode="DE" term="%22Bipartite+graphs%22">Bipartite graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Matching+theory%22">Matching theory</searchLink>
– Name: Abstract
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  Data: Casselgren, Markstörm, and Pham conjectured that any precolored distance-2 matching in the d -dimensional cube Q d with at most d colors can be extended to a proper d -edge-coloring. In this paper, we prove this conjecture and some related theorems. Especially, our result establishes that if G is a bipartite graph, then a precolored distance-2 matching in the Cartesian product H = G □ K 2 m with at most χ ′ (H) = Δ (H) = Δ (G) + 2 m − 1 colors can be extended to an edge-coloring using at most χ ′ (H) colors. As another generalization, we establish a similar result for the Cartesian product G □ K 1 , m . [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.dam.2026.02.041
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 4
        StartPage: 33
    Subjects:
      – SubjectFull: Hypercubes
        Type: general
      – SubjectFull: Graph coloring
        Type: general
      – SubjectFull: Bipartite graphs
        Type: general
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Matching theory
        Type: general
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      – TitleFull: Extending edge-colorings of distance-2 matchings in the hypercube.
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            – D: 15
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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              Value: 387
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            – TitleFull: Discrete Applied Mathematics
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