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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Constraints on the number of maximal independent sets in graphs
TL;DR: This work proves two conjectures, suggested by P. Erdos, that the maximum number of maximal independent sets among all graphs of order n in a family Φ is o(3n/3) ifΦ is either a family of connected graphs such that the largest value of maximum degrees among all graph n in Φ are o(n) or a family that approaches infinity as n → ∞.
Incorporating domain knowledge in latent topic models
TL;DR: Novel methods for enabling topic models to take advantage of side information, domain knowledge, and user guidance and feedback are developed to enhance topic model analyses across a variety of datasets, including non-text domains.
Book ChapterDOI
Worst case bounds for some NP-Complete modified Horn-SAT problems
TL;DR: An exact deterministic algorithm is provided showing that SAT for mixed (hidden) Horn formulas containing n variables is solvable in time O(2) and a fixed-parameter tractability classification for SAT restricted to mixed Horn formulas is obtained.
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Extremal Theorems for Databases
TL;DR: It is shown, that the maximum of the minimum number of rows, that are needed to represent a Sperner system of only two element sets is 3(n/3+o(n)).
References
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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.
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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.
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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.