It is shown that any n-chromatic graph is a full subdirect product of copies of the complete graphs Kn and Kn+1, except for some easily described graphs which are full subdirect products of copies of Kn+1 − {◦–◦} and Kn+2 − {◦–◦}; full means here that the projections of the decomposition are epimorphic in edges. This improves some results of Sabidussi. Subdirect powers of Kn or Kn+1 − {◦–◦} are...

In this paper we illustrate how nondeterminism can be used conveniently and effectively in designing efficient deterministic algorithms. In particular, our method gives a parameterized algorithm of running time O((5.7k)kn) for the 3-D matching problem, which significantly improves the previous algorithm by Downey et al. The algorithm can be generalized to yield an improved algorithm for the r -...

A double Dudeney set in Kn is a multiset of Hamilton cycles in Kn having the property that each 2-path in Kn lies in exactly two of the cycles. In this paper, we construct a double Dudeney set in Kn when n = p1p2 · · · ps + 2, where p1, p2, . . . , ps are different odd prime numbers and s is a natural number.

In this paper, for any prime p 11, we consider Cp-decompositions of Km × Kn and Km ∗ Kn and also Cp-factorizations of Km × Kn, where × and ∗ denote the tensor product and wreath product of graphs, respectively, (Km ∗ Kn is isomorphic to the complete m-partite graph in which each partite set has exactly n vertices). It has been proved that for m, n 3, Cp-decomposes Km ×Kn if and only if (1) eith...

In [2], [3], S. Gersten has introduced higher i£-groups of a ring which satisfy properties analogous to those of a generalized homology theory in a suitably defined homotopy category of rings [ l ] . In this announcement we use Gersten's i£-groups to define for a ring R a generalized cohomology theory KR( ), analogous to the AtiyahHirzebruch i£-theory, on the category of finite simplicial sets ...

Seymour conjectured for a fixed integer k ≥ 2 that if G is a graph of order n with δ(G) ≥ kn/(k + 1), then G contains the kth power Ck n of a Hamiltonian cycle Cn of G, and this minimum degree condition is sharp. Earlier the k = 2 case was conjectured by Pósa. This was verified by Komlós et al. [4]. For s ≥ 3, a graph is K1,s-free if it does not contain an induced subgraph isomorphic to K1,s. S...