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%2F24%3A10493093" target="_blank" >RIV/00216208:11320/24:10493093 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=2N42.QvDcd" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=2N42.QvDcd</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00026-023-00674-y" target="_blank" >10.1007/s00026-023-00674-y</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 = (x(1),..., x(n)) in a graph G is k-symmetric, if the mapping x(i) -&gt; 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 x(1),..., 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 degrees/k wedge of the drawing. The maximum k for which there exists a k-symmetric Hamilton cycle in G is referred to 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 constructed cycles 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 = (x(1),..., x(n)) in a graph G is k-symmetric, if the mapping x(i) -&gt; 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 x(1),..., 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 degrees/k wedge of the drawing. The maximum k for which there exists a k-symmetric Hamilton cycle in G is referred to 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 constructed cycles 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

J_imp - Článek v periodiku v databázi Web of Science

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

2024

Kód důvěrnosti údajů

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

Název periodika

Annals of Combinatorics

ISSN

0218-0006

e-ISSN

0219-3094

Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

59

Strana od-do

379-437

Kód UT WoS článku

001123435000001

EID výsledku v databázi Scopus

2-s2.0-85179724801