## 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__β²,__v__β²) iff both __u__ __u__β² β __E__(__G__) and __v__ __v__β² β __E__(__H__). Let __A__(__G__) denote the limit of the independence ratios of ten
Projectivity and independent sets in powers of graphs
β 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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β¦ 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: 162β171, 2002
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## Abstract Let __G__ be a connected, nonbipartite vertexβtransitive 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
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.