Isolation of Cycles

For any graph G , let ι c ( G ) denote the size of a smallest set D of vertices of G such that the graph obtained from G by deleting the closed neighbourhood of D contains no cycle. We prove that if G is a connected n -vertex graph that is not a triangle, then ι c ( G ) ≤ n / 4 . We also show that t...

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Vydáno v:Graphs and combinatorics Ročník 36; číslo 3; s. 631 - 637
Hlavní autor: Borg, Peter
Médium: Journal Article
Jazyk:angličtina
Vydáno: Tokyo Springer Japan 01.05.2020
Springer Nature B.V
Témata:
Apexes
Combinatorics
Engineering Design
Graph theory
Mathematics
Mathematics and Statistics
Original Paper
Graph domination
05C69
05C35
Cycle
Isolating set
05C38
ISSN:0911-0119, 1435-5914
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Popis
Shrnutí:For any graph G , let ι c ( G ) denote the size of a smallest set D of vertices of G such that the graph obtained from G by deleting the closed neighbourhood of D contains no cycle. We prove that if G is a connected n -vertex graph that is not a triangle, then ι c ( G ) ≤ n / 4 . We also show that the bound is sharp. Consequently, this settles a problem of Caro and Hansberg.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-020-02143-2