It is proved that a graph of order n contains a triangle if |N(X )| > 1 3 (n+|X |) for every independent set X of vertices. This bound is sharp.
โฆ LIBER โฆ
Irredundant and perfect neighbourhood sets in trees
โ Scribed by E.J. Cockayne; S.M. Hedetniemi; S.T. Hedetniemi; C.M. Mynhardt
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 373 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
For any tree T, it is proved that 0(T), the smallest cardinality of a perfect neighbourhood set, is bounded above by ir(T), the smallest cardinality of a maximal irredundant set.
๐ SIMILAR VOLUMES
Triangles and Neighbourhoods of Independ
โ
Andrew M. Robertshaw; Douglas R. Woodall
๐
Article
๐
2000
๐
Elsevier Science
๐
English
โ 124 KB
Perfect pairs of trees in graphs
โ
Ladislav Novak; Alan Gibbons
๐
Article
๐
1992
๐
John Wiley and Sons
๐
English
โ 392 KB
Independent perfect domination sets in C
โ
Jaeun Lee
๐
Article
๐
2001
๐
John Wiley and Sons
๐
English
โ 92 KB
๐ 1 views
## Abstract In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that the hypercube __Q~n~__ has an independent perfect domination set if and only if __Q~n~__ i
L-Regularity of Markov Sets and of m-Per
โ
Leokadia Bialas-Ciez; Raimondo Eggink
๐
Article
๐
2007
๐
Springer
๐
English
โ 221 KB
Does living in a poor neighbourhood resu
โ
Gwen van Eijk
๐
Article
๐
2010
๐
Springer Netherlands
๐
English
โ 175 KB
Stable Set Bonding in Perfect Graphs and
โ
D.G. Corneil; J. Fonlupt
๐
Article
๐
1993
๐
Elsevier Science
๐
English
โ 486 KB