In response to a problem of Voloshin, we find recursive formulae for the chromatic polyno-mials of complete r-uniform interval hypergraphs and cohypergraphs. We also give recursive formulae for the chromatic polynomials of complete 3-uniform and 4-uniform interval bihy-pergraphs and comment on the challenges for general r. Our method is to exploit the uniform and complete structure of these hyp...

Classical random walks on well-behaved graphs are rapidly mixing towards the uniform distribution. Moore and Russell showed that a continuous quantum walk on the hypercube is instantaneously uniform mixing. We show that the continuous-time quantum walks on other well-behaved graphs do not exhibit this uniform mixing. We prove that the only graphs amongst balanced complete multipartite graphs th...

In this paper we present an optimal algorithm for scheduling complete k-ary tree on two uniform processors of di erent speeds in order to minimize schedule length. We consider the basic case of unit standard execution times and unit communication times.

Let H be a hypergraph. For a k-edge coloring c : E(H) → {1, . . . , k} let f(H, c) be the number of components in the subhypergraph induced by the color class with the least number of components. Let fk(H) be the maximum possible value of f(H, c) ranging over all k-edge colorings of H . If H is the complete graph Kn then, trivially, f1(Kn) = f2(Kn) = 1. In this paper we prove that for n ≥ 6, f3...

Context-sensitive grammars in which each rule is of the forln aZfl-~ (-*Tfl are acyclic if the associated context-free grammar with the rules Z ~ 3' is acyclic. The problem whether an intmt string is in the language generated by an acyclic context-sensitive grammar is NP-conlplete.

We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (IIR) uniform filter banks (FB’s). Our analysis is based on a new relationship between the FB’s polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FB’s providing perfect reconstruction....

We say a s-uniform r-partite hypergraph is complete, if it has a vertex partition {V1, V2, . . . , Vr} of r classes and its hyperedge set consists of all the s-subsets of its vertex set which have at most one vertex in each vertex class. We denote the complete s-uniform r-partite hypergraph with k vertices in each vertex class by Ts,r(k). In this paper we prove that if h, r and s are positive i...

In this paper, we consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the 2n − 1 one-factors of a one-factorization of the complete graph K2n in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph. This property is termed sequentially uniform;...

We conjecture that for any fixed r and sufficiently large n, there is a monochromatic Hamiltonian Bergecycle in every (r − 1)-coloring of the edges of K n , the complete r-uniform hypergraph on n vertices. We prove the conjecture for r = 3, n 5 and its asymptotic version for r = 4. For general r we prove weaker forms of the conjecture: there is a Hamiltonian Berge-cycle in (r−1)/2 -colorings of...

A hypergraph H on n nodes is complete 3-uniform if the hyperedges are precisely the set of all node triples. A one-factor of H is a set of hyperedges that cover each node exactly once. According to Baranyai's proof, the hyperedges of H can be partitioned into one-factors iff n ≡ 0 (mod 3). Though the proof is constructive, it leads to an O(2)-time algorithm. We investigate a method for computin...