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

Result language
angličtina
Original language name
The Hamilton Compression of Highly Symmetric Graphs
Original language description
We say that a Hamilton cycle C = (x(1),..., 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 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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