Characterization and recognition of Radon-independent sets in split graphs
✍ Scribed by Dourado, Mitre C.; Rautenbach, Dieter; dos Santos, Vinícius Fernandes; Szwarcfiter, Jayme L.
- Book ID
- 118201140
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 191 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0020-0190
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## Abstract We investigate the relationship between projectivity and the structure of maximal independent sets in powers of circular graphs, Kneser graphs and truncated simplices. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 162–171, 2002
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.
Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,