Let G = (V, E) be a digraph and f a mapping from E into an Abelian group A. Associated with f is its boundary aS, a mapping from V to A, defined by af(x) = c Dleavingxf(e)-Ceenteringx f(e). We sayâ€¦ (More)

An H-decomposition of a graph G = (V,E) is a partition of E into subgraphs isomorphic to H. Given a fixed graph H, the H-decomposition problem is to determine whether an input graph G admits anâ€¦ (More)

Let u1 , â€¢â€¢â€¢ , u. and v1, â€¢â€¢â€¢ , v. be bases of a vector space (the interesting case, when the underlying field is finite). Then there exist vectors w1, â€¢â€¢â€¢ , w._ 1 such that every n consecutiveâ€¦ (More)

It is proved that the dlrecUonal algorithm for solving a game tree is optimal, in the sense of average run trine, for balanced trees (a family containing all uniform trees). This result implies thatâ€¦ (More)

Notice that there are easy examples showing that the assertion of the con, jecture is false for q~_3. We have reached this conjecture while trying to generalize some simple properties o f sparseâ€¦ (More)

An H-decomposition of a graph G = (V,E) is a partition of E into subgraphs isomorphic to H. Given a fixed graph H, the H-decomposition problem is to determine whether an input graph G admits anâ€¦ (More)