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Projectivity and independent sets in powers of graphs

✍ Scribed by Benoit Larose; Claude Tardif


Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
95 KB
Volume
40
Category
Article
ISSN
0364-9024

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✦ Synopsis


Abstract

We investigate the relationship between projectivity and the structure of maximal independent sets in powers of circular graphs, Kneser graphs and truncated simplices. Β© 2002 Wiley Periodicals, Inc. J Graph Theory 40: 162–171, 2002


πŸ“œ SIMILAR VOLUMES


Independent sets in tensor graph powers
✍ Alon, Noga (author);Lubetzky, Eyal (author) πŸ“‚ Article πŸ“… 2006 πŸ› Wiley-Liss Inc. 🌐 English βš– 154 KB

## Abstract The tensor product of two graphs, __G__ and __H__, has a vertex set __V__(__G__) Γ— __V__(__H__) and an edge between (__u__,__v__) and (__u__β€²,__v__β€²) iff both __u__ __u__β€² ∈ __E__(__G__) and __v__ __v__β€² ∈ __E__(__H__). Let __A__(__G__) denote the limit of the independence ratios of ten

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Independent sets in tensor graph powers
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Independent sets of maximal size in tens
✍ Cheng Yeaw Ku; Benjamin B. McMillan πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 97 KB πŸ‘ 2 views

## Abstract Let __G__ be a connected, nonbipartite vertex‐transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product __G__ Γ— __G__ are the preimages of the independent sets of maximal cardinality in __G__ under projections, then the same holds for all

Triangles and Neighbourhoods of Independ
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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.