The number of maximal independent sets in a connected graph
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The maximum number of maximal independent sets which a connected graph on n vertices can have is determined, and the extremal graphs are completely characterize, thereby answering a question of Wilf.About:
This article is published in Discrete Mathematics.The article was published on 1988-02-01 and is currently open access. It has received 92 citations till now. The article focuses on the topics: Maximal independent set & Independent set.read more
Citations
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Proceedings ArticleDOI
SDN-Based Efficient Bandwidth Allocation for Caching Enabled Cognitive Radio Networks
TL;DR: Extensive simulations show that SDM-CRN can efficiently utilize the bandwidth and improve the user experience in multi-hop CRNs and conjecture that this problem is NP-hard, and propose a heuristic algorithm.
Journal ArticleDOI
On the Maximum Number of Maximum Independent Sets
Elena Mohr,Dieter Rautenbach +1 more
TL;DR: A very short and simple proof of Zykov’s generalization of Turán's theorem, which implies that the number of maximum independent sets of a graph of order n and independence number α with α at most is at most at most.
Journal ArticleDOI
On the maximum number of maximum independent sets in connected graphs
Elena Mohr,Dieter Rautenbach +1 more
TL;DR: In this paper, the authors characterize the connected graphs of given order n and given independence number α that maximize the number of maximum independent sets of a given graph. But they do not characterize the graphs that arise from the disjoint union of cliques of orders n and α.
Journal ArticleDOI
Efficient Conversion of RNA Pseudoknots to Knot-Free Structures Using a Graphical Model
TL;DR: The pseudoknot removal problem was transformed into a circle graph maximum weight independent set (MWIS) problem, in which each MWIS represents a unique optimal deknotted structure and an existing circle graph MWIS algorithm was extended to report either single or all solutions.
Book ChapterDOI
Extremal Theorems for Databases
TL;DR: It is shown, that the maximum of the minimal number of tuples, that are needed to represent a Sperner system of only two element sets is 3(n/3+o(n)).
References
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Journal ArticleDOI
On cliques in graphs
J. W. Moon,L. Moser +1 more
TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Journal ArticleDOI
The number of maximal independent sets in a tree
TL;DR: In this paper, the maximal independent sets of vertices that any tree of n vertices can have were shown to have maximal number of maximal independent vertices, where vertices are independent sets.
Journal ArticleDOI
The number of maximal independent sets in connected graphs
TL;DR: A theorem of Moon and Moser is generalized to determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50.