Flips in colorful triangulations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509913" target="_blank" >RIV/00216208:11320/25:10509913 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=PQ1PguWcpk" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=PQ1PguWcpk</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.20382/jocg.v16i1a9" target="_blank" >10.20382/jocg.v16i1a9</a>
Alternative languages
Result language
angličtina
Original language name
Flips in colorful triangulations
Original language description
The associahedron is the graph G(N) that has as nodes all triangulations of a convex N-gon, and an edge between any two triangulations that differ in a flip operation. A flip removes an edge shared by two triangles and replaces it by the other diagonal of the resulting 4-gon. In this paper, we consider a large collection of induced subgraphs of G(N) obtained by Ramsey-type colorability properties. Specifically, coloring the points of the N-gon red and blue alternatingly, we consider only colorful triangulations, namely triangulations in which every triangle has points in both colors, i.e., monochromatic triangles are forbidden. The resulting induced subgraph of G(N) on colorful triangulations is denoted by F(N). We prove that F(N) has a Hamilton cycle for all N >= 8, resolving a problem raised by Sagan, i.e., all colorful triangulations on N points can be listed so that any two cyclically consecutive triangulations differ in a flip. In fact, we prove that for an arbitrary fixed coloring pattern of the N points with at least 10 changes of color, the resulting subgraph of G(N) on colorful triangulations (for that coloring pattern) admits a Hamilton cycle. We also provide an efficient algorithm for computing a Hamilton path in F(N) that runs in time O(1) on average per generated node. This algorithm is based on a new and algorithmic construction of a tree rotation Gray code for listing all n-vertex k-ary trees that runs in time O(k) on average per generated tree.
Czech name
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Czech description
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Classification
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)
Result continuities
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)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Computational Geometry
ISSN
1920-180X
e-ISSN
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Volume of the periodical
16
Issue of the periodical within the volume
1
Country of publishing house
CA - CANADA
Number of pages
38
Pages from-to
295-332
UT code for WoS article
001482914100001
EID of the result in the Scopus database
2-s2.0-105006563166