Barnetteâ€™s conjecture is the statement that every cubic 3-connected bipartite planar graph is Hamiltonian. We show that if such a graph has a 2-factor F which consists only of facial 4-cycles, thenâ€¦ (More)

Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number ofâ€¦ (More)

Let us consider the interval [0, 1) as a billiard table rectangle with perimeter 1 and a sequence F(m) âˆˆ [0, 1),m âˆˆ N âˆª {0}, of successive rebounds of a billiard ball against the sides of a billiardâ€¦ (More)