The Hamilton Compression of Highly Symmetric Graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The Hamilton Compression of Highly Symmetric Graphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Hamilton Compression of Highly Symmetric Graphs

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GA22-15272S" target="_blank" >GA22-15272S: Principy kombinatorického generování</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-256-3

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

14

Strana od-do

1-14

Název nakladatele

Schloss Dagstuhl - Leibniz-Zentrum für Informatik

Místo vydání

Dagstuhl, Německo

Místo konání akce

Vienna

Datum konání akce

22. 8. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—