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Independence number and the complexity of families of sets

✍ Scribed by D.Q. Naiman; H.P. Wynn


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
870 KB
Volume
154
Category
Article
ISSN
0012-365X

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Some results on the complexity of famili
✍ Daniel Grieser πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 872 KB

Grieser, D., Some results on the complexity of families of sets, Discrete Mathematics 88 (1991) 179-192. Let 'Y be a property of graphs on a fixed n-element vertex set V. The complexity c(P) is the minimal number of edges whose existence in a previously unknown graph H has to be tested such that it

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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,

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A subset of vertices is a maximum independent set if no two of the vertices are joined by an edge and the subset has maximum cardinality. In this paper we answer a question posed by Herb Wilf. We show that the greatest number of maximum independent sets for a tree of n vertices is 2(n-3\* for odd n

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## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. ErdΓΆs, that the maximum number of m

The number of maximal independent sets i
✍ Jerrold R. Griggs; Charles M. Grinstead; David R. Guichard πŸ“‚ Article πŸ“… 1988 πŸ› Elsevier Science 🌐 English βš– 1021 KB

We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S