On the number of maximal independent sets in a graph

Miller and Muller (1960) and independently Moon and Moser (1965) determined the maximum number of maximal independent sets in an n -vertex graph. We give a new and simple proof of this result.

[1]  Coenraad Bron,et al.  Finding all cliques of an undirected graph , 1973 .

[2]  Ulrich Berger,et al.  Modified bar recursion , 2006, Mathematical Structures in Computer Science.

[3]  David Eppstein.  Small Maximal Independent Sets and Faster Exact Graph Coloring , 2001, WADS.

[4]  Vincent Vatter.  Maximal Independent Sets and Separating Covers , 2011, Am. Math. Mon..

[5]  Eugene L. Lawler,et al.  Generating all Maximal Independent Sets: NP-Hardness and Polynomial-Time Algorithms , 1980, SIAM J. Comput..

[6]  Anna Pagh,et al.  Solving the String Statistics Problem in Time O(n log n) , 2002, ICALP.

[7]  Mihalis Yannakakis,et al.  On Generating All Maximal Independent Sets , 1988, Inf. Process. Lett..

[8]  J. Moon,et al.  On cliques in graphs , 1965 .

[9]  F. Jones.  There and back again , 1989, Nature.

[10]  Aske Simon Christensen,et al.  Extending Java for high-level Web service construction , 2002, TOPL.

[11]  Olivier Danvy,et al.  Syntactic Theories in Practice , 2001, RULE@PLI.

[12]  Shuji Tsukiyama,et al.  A New Algorithm for Generating All the Maximal Independent Sets , 1977, SIAM J. Comput..

[13]  Ronald Cramer,et al.  Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups , 2002, CRYPTO.

[14]  Anna Ingólfsdóttir,et al.  A Formalization of Linkage Analysis , 2002 .

[15]  U. Kohlenbach.  Uniform asymptotic regularity for Mann iterates , 2002 .

[16]  Serge Gaspers,et al.  Exponential Time Algorithms - Structures, Measures, and Bounds , 2010 .

[17]  Olivier Danvy,et al.  On one-pass CPS transformations , 2002, Journal of Functional Programming.

[18]  Akira Tanaka,et al.  The worst-case time complexity for generating all maximal cliques and computational experiments , 2006, Theor. Comput. Sci..

[19]  Z. Ésik,et al.  Equational Axioms for Probabilistic Bisimilarity (Preliminary Report) , 2002 .

[20]  Zsolt Tuza,et al.  The Number of Maximal Independent Sets in Triangle-Free Graphs , 1993, SIAM J. Discret. Math..

[21]  J. Nielsen.  On the Number of Maximal Independent Sets in a Graph , 2002 .

[22]  David Eppstein,et al.  Listing All Maximal Cliques in Sparse Graphs in Near-optimal Time , 2010, Exact Complexity of NP-hard Problems.