COMBINATORICS
1999
13 years 11 months ago
1999
An orthogonal coloring of a graph G is a pair {c1, c2} of proper colorings of G, having the property that if two vertices are colored with the same color in c1, then they must hav...
COMBINATORICS
1999
13 years 11 months ago
1999
COMBINATORICS
1999
13 years 11 months ago
1999
![A [k, k+1]-Factor Containing A Given Hamiltonian Cycle](https://www.sciweavers.org/files/imagecache/thumbnail/imagecache/a_k_k_1_factor_containing_a_given_hamiltonian_cycle_COMBINATORICS_1999.jpg "A [k, k+1]-Factor Containing A Given Hamiltonian Cycle")
We prove the following best possible result. Let k 2 be an integer and G be a graph of order n with minimum degree at least k. Assume n 8k - 16 for even n and n 6k-13 for odd n...
COMBINATORICS
1999
13 years 11 months ago
1999
Abstract. We generalize Ehrhart's idea ([Eh]) of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n + 1...
COMBINATORICS
1999
13 years 11 months ago
1999
Let m and n be positive integers, and let R = (r1, . . . , rm) and S = (s1, . . . , sn) be non-negative integral vectors. Let A(R, S) be the set of all m
COMBINATORICS
1999
13 years 11 months ago
1999
Abstract. Consider, for a permutation Sk, the number F(n, ) of permutations in Sn which avoid as a subpattern. The conjecture of Stanley and Wilf is that for every there is a c...
COMBINATORICS
1999
13 years 11 months ago
1999
We say that an antichain A in the boolean lattice Bn is flat if there exists
COMBINATORICS
1999
13 years 11 months ago
1999
We show that if P(x) is a polynomial with nondecreasing, nonnegative coefficients, then the coefficient sequence of P(x + 1) is unimodal. Applications are given.
COMBINATORICS
1999
13 years 11 months ago
1999
COMBINATORICS
1999
13 years 11 months ago
1999
An asymptotic estimate is given for the coefficients of products of large powers of generating functions. This theorem and another local limit theorem which is useful for conditio...