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,
Maximal independent sets in bipartite graphs
β Scribed by Jiuqiang Liu
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 458 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
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. In this paper, we determine the maximum number of maximal independent sets among all bipartite graphs of order n and the extremal graphs as well as the corresponding results for connected bipartite graphs. Β© 1993 John Wiley & Sons, Inc.
π SIMILAR VOLUMES
## 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
## Abstract We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with __n__ vertices and at most __r__ cycles. The second family is all graphs of the first family which are connected and satisfy __n__ββ₯β3__r__. Β© 2006 Wiley Period
## Abstract It is proven that each maximal planar bipartite graph is decomposable into two trees. Β© 1993 John Wiley & Sons, Inc.
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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