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The Hamilton compression of highly symmetric graphs
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Gregor, Petr, Merino, Arturo and Mutze, Torsten (2022) The Hamilton compression of highly symmetric graphs. In: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022), Vienna, Austria, 22—26 Aug 2022, 241 54:1-54:14. ISBN 9783959772563. doi:10.4230/LIPIcs.MFCS.2022.54 ISSN 1868-8969.
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Official URL: https://drops.dagstuhl.de/opus/volltexte/2022/1685...
Abstract
We say that a Hamilton cycle C = (x₁,…,x_n) in a graph G is k-symmetric, if the mapping x_i ↦ x_{i+n/k} for all i = 1,…,n, where indices are considered modulo n, is an automorphism of G. In other words, if we lay out the vertices x₁,…,x_n equidistantly on a circle and draw the edges of G as straight lines, then the drawing of G has k-fold rotational symmetry, i.e., all information about the graph is compressed into a 360^∘/k wedge of the drawing. We refer to the maximum k for which there exists a k-symmetric Hamilton cycle in G as the Hamilton compression of G. We investigate the Hamilton compression of four different families of vertex-transitive graphs, namely hypercubes, Johnson graphs, permutahedra and Cayley graphs of abelian groups. In several cases we determine their Hamilton compression exactly, and in other cases we provide close lower and upper bounds. The cycles we construct have a much higher compression than several classical Gray codes known from the literature. Our constructions also yield Gray codes for bitstrings, combinations and permutations that have few tracks and/or that are balanced.
Item Type: | Conference Item (Paper) | ||||||||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Graph theory , Combinatorial analysis , Gray codes , Hypercube , Cayley graphs , Abelian groups | ||||||||||||||||||
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) | ||||||||||||||||||
Publisher: | Schloss Dagstuhl — Leibniz-Zentrum für Informatik | ||||||||||||||||||
Place of Publication: | Dagstuhl, Germany | ||||||||||||||||||
ISBN: | 9783959772563 | ||||||||||||||||||
ISSN: | 1868-8969 | ||||||||||||||||||
Official Date: | 22 August 2022 | ||||||||||||||||||
Dates: |
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Volume: | 241 | ||||||||||||||||||
Page Range: | 54:1-54:14 | ||||||||||||||||||
DOI: | 10.4230/LIPIcs.MFCS.2022.54 | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
Date of first compliant deposit: | 10 November 2022 | ||||||||||||||||||
Date of first compliant Open Access: | 11 November 2022 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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Conference Paper Type: | Paper | ||||||||||||||||||
Title of Event: | 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) | ||||||||||||||||||
Type of Event: | Conference | ||||||||||||||||||
Location of Event: | Vienna, Austria | ||||||||||||||||||
Date(s) of Event: | 22—26 Aug 2022 | ||||||||||||||||||
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