Tree pattern matching is a fundamental problem that has a wide range of applications in Web data management, XML processing, and selective data dissemination. In this paper we develop efficient algorithms for the tree homeomorphism problem, i.e., the problem of matching a tree pattern with exclusively transitive (descendant) edges. We first prove that deciding whether there is a tree homeomorph...

With each isolating block for a homeomorphism of an orientable manifold we associate a cup product pairing. Up to an isomorphism, this is a pairing of the discrete Conley indices of the homeomorphism and its inverse on the isolating block. We show that this pairing is nondegenerate. As a corollary we prove a time duality result for the discrete Conley index. 0. Introduction The observation that...

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into sets Π1, . . . ,Πk, where Πi, i ∈ [k], is an i-packing. The following conjecture is posed and studied: if G is a subcubic graph, then χρ(S(G)) ≤ 5, where S(G) is the subdivision of G. The conjecture is proved for all generalized prisms of cycles. To get this result it ...

We study expansive dynamical systems in the setting of distributive lattices and their automorphisms, usual notion expansiveness for a homeomorphism compact metric space being particular case when lattice is topology phase ordered by inclusion automorphism one induced homeomorphism, mapping open sets to sets. prove this context generalizations Mañé's Theorem Utz's about finite dimensionality an...