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» Independence in Direct-Product Graphs
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APPROX
2004
Springer
179views Algorithms» more  APPROX 2004»
14 years 23 days ago
Maximum Weight Independent Sets and Matchings in Sparse Random Graphs. Exact Results Using the Local Weak Convergence Method
ABSTRACT: Let G(n, c/n) and Gr(n) be an n-node sparse random graph and a sparse random rregular graph, respectively, and let I(n, r) and I(n, c) be the sizes of the largest indepen...
David Gamarnik, Tomasz Nowicki, Grzegorz Swirszcz
DM
2000
99views more  DM 2000»
13 years 7 months ago
Chromatically unique bipartite graphs with low 3-independent partition numbers
For integers p; q; s with p
Feng Ming Dong, Khee Meng Koh, Kee L. Teo, Charles...
SIAMDM
1998
165views more  SIAMDM 1998»
13 years 7 months ago
The Number of Independent Sets in a Grid Graph
If f(m, n) is the (vertex) independence number of the m × n grid graph, then we show that the double limit η = def limm,n→∞ f(m, n) 1 mn exists, thereby refining earlier res...
Neil J. Calkin, Herbert S. Wilf
SODA
2010
ACM
234views Algorithms» more  SODA 2010»
14 years 4 months ago
PTAS for maximum weight independent set problem with random weights in bounded degree graphs
Finding the largest independent set in a graph is a notoriously difficult NP-complete combinatorial optimization problem. Moreover, even for graphs with largest degree 3, no polyn...
David Gamarnik, David Goldberg, Theophane Weber
DAM
2011
13 years 2 months ago
Independence in connected graphs
We prove that if G = (VG, EG) is a finite, simple, and undirected graph with κ components and independence number α(G), then there exist a positive integer k ∈ N and a functi...
Jochen Harant, Dieter Rautenbach