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SIAMDM
1998
165views more  SIAMDM 1998»
14 years 9 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
JUCS
2006
94views more  JUCS 2006»
14 years 9 months ago
Completeness in the Boolean Hierarchy: Exact-Four-Colorability, Minimal Graph Uncolorability, and Exact Domatic Number Problems
: This paper surveys some of the work that was inspired by Wagner's general technique to prove completeness in the levels of the boolean hierarchy over NP and some related res...
Tobias Riege, Jörg Rothe
DAM
1999
105views more  DAM 1999»
14 years 9 months ago
The b-chromatic Number of a Graph
The achromatic number (G) of a graph G = (V, E) is the maximum k such that V has a partition V1, V2, . . . , Vk into independent sets, the union of no pair of which is independent...
Robert W. Irving, David Manlove
EJC
2008
14 years 10 months ago
The distinguishing number of Cartesian products of complete graphs
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesi...
Wilfried Imrich, Janja Jerebic, Sandi Klavzar
ENDM
2008
118views more  ENDM 2008»
14 years 10 months ago
Number of Crossing-Free Geometric Graphs vs. Triangulations
We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...
Andreas Razen, Jack Snoeyink, Emo Welzl