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Avoiding edge colorings of hypercubes
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics.
2019 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
Abstract [en]

The hypercube Qn is the graph whose vertices are the ordered n-tuples of zeros and ones, where two vertices are adjacent iff they differ in exactly one coordinate. A partial edge coloring f of a graph G is a mapping from a subset of edges of G to a set of colors; it is called proper if no pair of adjacent edges share the same color. A (possibly partial and unproper) coloring f is avoidable if there exists a proper coloring g such that no edge has the same color under f and g. An unavoidable coloring h is called minimal if it would be avoidable by letting any colored edge turn noncolored.

We construct a computer program to find all minimal unavoidable edge colorings of Q3 using up to 3 colors, and draw some conclusions for general Qn.

Place, publisher, year, edition, pages
2019. , p. 73
Keywords [en]
Graph Theory, Hypercubes, Avoiding edge colorings
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-160863ISRN: LiTH-MAT-EX--2019/07--SEOAI: oai:DiVA.org:liu-160863DiVA, id: diva2:1360216
Subject / course
Mathematics
Presentation
2019-09-13, Kompakta rummet, 10:15 (English)
Supervisors
Examiners
Available from: 2019-11-11 Created: 2019-10-11 Last updated: 2019-11-11Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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Output format
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