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131
Voted
COMBINATORICS
2004
15 years 3 months ago
2004
It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at l...
139
Voted
COMBINATORICS
2004
15 years 3 months ago
2004
In 1958, Richard Guy proved that the number of partitions of n into odd parts greater than one equals the number of partitions of n into distinct parts with no powers of 2 allowed...
113
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
Let n be the fraction of structures of size" n which are connected"; e.g., a the fraction of labeled or unlabeled n-vertex graphshavingone component, b the fraction of p...
116
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
Let (G) denote the domination number of a graph G and let G H denote the Cartesian product of graphs G and H. We prove that (G)(H) 2(G H) for all simple graphs G and H. 2000 Math...
117
Voted
COMBINATORICS
2000
15 years 3 months ago
2000
Given an integer n 2, and a non-negative integer k, consider all affine hyperplanes in Rn of the form xi = xj +r for i, j [n] and a non-negative integer r k. Let n,k be the pos...