On decreasing the orders of (k, g) -graphs
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On decreasing the orders of (k, g) -graphs
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
On decreasing the orders of (k, g) -graphs
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>SC</sub> - Článek v periodiku v databázi SCOPUS
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Journal of Combinatorial Optimization
ISSN
1382-6905
e-ISSN
1573-2886
Svazek periodika
46
Číslo periodika v rámci svazku
4
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
14
Strana od-do
26
Kód UT WoS článku
—
EID výsledku v databázi Scopus
2-s2.0-85177043143