A packing of a graph G is a set {G1, G2} such that G1 ∼= G, G2 ∼= G, and G1 and G2 are edge disjoint subgraphs of Kn. Let F be a family of graphs. A near packing admitting F of a graph G is a generalization of a packing. In a near packing admitting F , the two copies of G may overlap so the subgraph defined by the edges common to both copies is a member of F . In the paper we study three famili...

This paper proves that there does not exist a polynomial-time algorithm to the the subset sum problem. As this problem is in NP , the result implies that the class P of problems admitting polynomial-time algorithms does not equal the class NP of problems admitting nondeterministic polynomial-time algorithms.

We present an example of a fibred quadratic polynomial admitting an attracting invariant 2-curve. By an unfolding construction we obtain an example of a fibred quadratic polynomial admitting two attracting invariant curves. This phenomena can not occur in the non-fibred setting.