A dynamical system connected with an inhomogeneous 6-vertex model

Vertex Covers and Connected Vertex Covers in 3-connected Graphs

A vertex cover of a graph G=(V,E) is a subset N of V such that each element of E is incident upon some element of N, where V and E are the sets of vertices and of edges of G, respectively. A connected vertex cover of a graph G is a vertex cover of G such that the subgraph G[N] induced by N of G is connected. The minimum vertex cover problem (VCP) is the problem of finding a vertex cover of mini...

Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph

The connected forcing connected vertex detour number of a graph

For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdx(...

An inverse dynamical problem for connected beams

This paper deals with a dynamical inverse problem for a composite beam formed by two connected beams. The vibrations of the composite beam are governed by a differential system where a coupling takes place between longitudinal and bending motions. In this paper, we neglect bending motions and we only deal with the longitudinal motions. These motions are governed by a two-by-two second order sys...

The 6 Vertex Model and Schubert Polynomials

We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.