Local Algorithms, Regular Graphs of Large Girth, and Random Regular Graphs

We introduce a general class of algorithms and analyse their application to regular graphs of large girth. In particular, we can transfer several results proved for random regular graphs into (deterministic) results about all regular graphs with sufficiently large girth. This reverses the usual dire...

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Vydáno v:Combinatorica (Budapest. 1981) Ročník 38; číslo 3; s. 619 - 664
Hlavní autoři: Hoppen, Carlos, Wormald, Nicholas
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer
Springer Nature B.V
Témata:
Algorithms
Combinatorics
Graphs
Lower bounds
Mathematics
Mathematics and Statistics
Original Paper
05C80
05C69
05C35
05C85
ISSN:0209-9683, 1439-6912
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Shrnutí:We introduce a general class of algorithms and analyse their application to regular graphs of large girth. In particular, we can transfer several results proved for random regular graphs into (deterministic) results about all regular graphs with sufficiently large girth. This reverses the usual direction, which is from the deterministic setting to the random one. In particular, this approach enables, for the first time, the achievement of results equivalent to those obtained on random regular graphs by a powerful class of algorithms which contain prioritised actions. As a result, we obtain new upper or lower bounds on the size of maximum independent sets, minimum dominating sets, maximum k -independent sets, minimum k -dominating sets and maximum k -separated matchings in r -regular graphs with large girth.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-016-3236-x