We compute the Chow ring of the classifying space BSO(2n, C) in the sense of Totaro using the fibration Gl(2n)/SO(2n) → BSO(2n) → BGl(2n) and a computation of the Chow ring of Gl(2n)/SO(2n) in a previous paper. We find this Chow ring is generated by Chern classes and a characteristic class defined by Edidin and Graham which maps to 2 times the Euler class under the usual class map from the Chow...

At Eurocrypt ’96, Coppersmith proposed an algorithm for finding small roots of bivariate integer polynomial equations, based on lattice reduction techniques. But the approach is difficult to understand. In this paper, we present a much simpler algorithm for solving the same problem. Our simplification is analogous to the simplification brought by Howgrave-Graham to Coppersmith’s algorithm for f...

We show that if a graph G has the property that all subsets of vertices of size n/4 contain the “correct” number of triangles one would expect to find in a random graph G(n, 12 ), then G behaves like a random graph, that is, it is quasi-random in the sense of Chung, Graham, and Wilson [6]. This answers positively an open problem of Simonovits and Sós [10], who showed that in order to deduce tha...

Chung, Diaconis, and Graham considered random processes of the form Xn+1 = anXn + bn (mod p) where p is odd, X0 = 0, an = 2 always, and bn are i.i.d. for n = 0, 1, 2, . . .. In this paper, we show that if P (bn = −1) = P (bn = 0) = P (bn = 1) = 1/3, then there exists a constant c > 1 such that c log2 p steps are not enough to make Xn get close to uniformly distributed on the integers mod p.

Graham and Pollak proved that one needs at least n − 1 complete bipartite subgraphs (bicliques) to partition the edge set of the complete graph on n vertices. In this paper, we study the extension of Graham and Pollak’s result to coverings of a graph G where each edge of G is allowed to be covered a specified number of times and its generalization to complete uniform hypergraphs. We also discus...

The diameter of a graph is an important factor for communication as it determines the maximum communication delay between any pair of processors in a network. Graham and Harary [N. Graham, F. Harary, Changing and unchanging the diameter of a hypercube, Discrete Applied Mathematics 37/38 (1992) 265–274] studied how the diameter of hypercubes can be affected by increasing and decreasing edges. Th...

Distributions of pebbles to the vertices of a graph are said to be solvable when a pebble may be moved to any specified vertex using a sequence of admissible pebbling rules. The optimal pebbling number is the least number of pebbles needed to create a solvable distribution. We provide a simpler proof verifying Pachter, Snevily and Voxman’s determination of the optimal pebbling number of paths, ...

An edge of a graph is called critical, if deleting it the stability number of the graph increases, and a nonedge is called co-critical, if adding it to the graph the size of the maximum clique increases. We prove in this paper, that the minimal imperfect graphs containing certain configurations of two critical edges and one co-critical nonedge are exactly the odd holes or antiholes. Then we ded...

We prove that for every > 0 and positive integer r, there exists ∆0 = ∆0( ) such that if ∆ > ∆0 and n > n(∆, , r) then there exists a packing of Kn with b(n − 1)/∆c graphs, each having maximum degree at most ∆ and girth at least r, where at most n edges are unpacked. This result is used to prove the following: Let f be an assignment of real numbers to the edges of a graph G. Let α(G, f) denote ...

An application of Fourier descriptors and convex hull for shape analysis is presented. Convex hull is used for dividing a shape into small parts. Amplitude spectrum which is invariant to scaling, translation and choosing a starting point is obtained from the Fourier descriptors (see e.g [1-3]) and used for comparison. All calculations are performed with the author's software and some algorithms...