COMBINATORICS
2000
14 years 8 days ago
2000
A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) i...
COMBINATORICS
2000
14 years 8 days ago
2000
The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of oth...
COMBINATORICS
2000
14 years 8 days ago
2000
We deal, from a theoretical point of view, with the asymmetric Hamiltonian p
COMBINATORICS
2000
14 years 8 days 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...
COMBINATORICS
2000
14 years 8 days ago
2000
Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning...
COMBINATORICS
2000
14 years 8 days ago
2000
We give new lower bounds for the Schur numbers S(6) and S(7). This will imply new lower bounds for the Multicolor Ramsey Numbers R6(3) and R7(3). We also make several observations...
COMBINATORICS
2000
14 years 8 days ago
2000
A graph with diameter d is strongly distance-regular if is distanceregular and its distance-d graph d is strongly regular. The known examples are all the connected strongly regu...
COMBINATORICS
2000
14 years 8 days ago
2000
To each coherent configuration (scheme) C and positive integer m we associate a natural scheme C(m) on the m-fold Cartesian product of the point set of C having the same automorph...
COMBINATORICS
2000
14 years 8 days ago
2000
Abstract. We introduce color-signed permutations to obtain a very explicit combinatorial interpretation of the q-Eulerian identities of Brenti and some generalizations. In particul...
COMBINATORICS
2000
14 years 8 days ago
2000
We show that the linear discrepancy of a basic totally unimodular matrix A Rm