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A new backtracking algorithm for generating the family of maximal independent sets of a graph

โœ Scribed by E. Loukakis


Book ID
108020107
Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
636 KB
Volume
9
Category
Article
ISSN
0898-1221

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๐Ÿ“œ SIMILAR VOLUMES


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โœ Jerrold R. Griggs; Charles M. Grinstead; David R. Guichard ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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

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The present paper describes an algorithm for constructing families of k-independent subsets & of {1,2, . . . , n} with &I >2ck", where c, = d/(k -1)2& and d is a certain constant. The algorithm has a polynomial complexity with respect to the size of the family constructed.

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## Abstract Consider a family of chords in a circle. A circle graph is obtained by representing each chord by a vertex, two vertices being connected by an edge when the corresponding chords intersect. In this paper, we describe efficient algorithms for finding a maximum clique and a maximum indepen

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It is well known [9] that finding a maximal independent set in a graph is in class J%, and [lo] that finding a maximal independent set in a hypergraph with fixed dimension is in %JV"%' . It is not known whether this latter problem remains in A% when the dimension is part of the input. We will study