The Hamilton Compression of Highly Symmetric Graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10450700" target="_blank" >RIV/00216208:11320/22:10450700 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.MFCS.2022.54" target="_blank" >https://doi.org/10.4230/LIPIcs.MFCS.2022.54</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2022.54" target="_blank" >10.4230/LIPIcs.MFCS.2022.54</a>

Result language

angličtina

Original language name

The Hamilton Compression of Highly Symmetric Graphs

Original language description

We say that a Hamilton cycle C = (x1,...,xn) in a graph G is k-symmetric, if the mapping xi RIGHTWARDS ARROW xi+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,...,xn 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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA22-15272S" target="_blank" >GA22-15272S: Principles of combinatorial generation</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-256-3

ISSN

1868-8969

e-ISSN

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Number of pages

14

Pages from-to

1-14

Publisher name

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl, Německo

Event location

Vienna

Event date

Aug 22, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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