Edge precoloring extension of hypercubes

We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most d−1 edges of the d‐dimension...

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Bibliographic Details
Published in:Journal of graph theory 2020-11, Vol.95 (3), p.410-444
Main Authors: Casselgren, Carl Johan, Markström, Klas, Pham, Lan Anh
Format: Article
Language:English
Subjects:
Arrays
Coloring
edge coloring
hypercube
Hypercubes
matematik
Mathematics
precoloring extension
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Summary:We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most d−1 edges of the d‐dimensional hypercube Qd can be extended to a proper d‐edge coloring of Qd. Additionally, we characterize which partial edge colorings of Qd with precisely d precolored edges are extendable to proper d‐edge colorings of Qd.
ISSN:0364-9024
1097-0118
1097-0118
DOI:10.1002/jgt.22561