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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Bibliographic Details
Published in:Graphs and combinatorics Vol. 36; no. 3; pp. 631 - 637
Main Author: Borg, Peter
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.05.2020
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-020-02143-2