On decreasing the orders of (k, g) -graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F23%3A10253327" target="_blank" >RIV/61989100:27240/23:10253327 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10878-023-01092-9" target="_blank" >https://link.springer.com/article/10.1007/s10878-023-01092-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10878-023-01092-9" target="_blank" >10.1007/s10878-023-01092-9</a>
Alternative languages
Result language
angličtina
Original language name
On decreasing the orders of (k, g) -graphs
Original language description
A (k, g) -graph is a k-regular graph of girth g . Given k>=2 and g>=3 , (k, g) -graphs of infinitely many orders are known to exist and the problem of finding a (k, g)-graph of the smallest possible order is known as the Cage Problem. The aim of our paper is to develop systematic (programmable) ways for lowering the orders of existing (k, g) -graphs, while preserving their regularity and girth. Such methods, in analogy with the previously used excision, may have the potential for constructing smaller (k, g)-graphs from current smallest examples-record holders-some of which have not been improved in years. In addition, we consider constructions that preserve the regularity, the girth and the order of the considered graphs, but alter the graphs enough to possibly make them suitable for the application of our order decreasing methods. We include a detailed discussion of several specific parameter cases for which several non-isomorphic smallest examples are known to exist, and address the question of the distance between these non-isomorphic examples based on the number of changes required to move from one example to another.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
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 Combinatorial Optimization
ISSN
1382-6905
e-ISSN
1573-2886
Volume of the periodical
46
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
26
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85177043143