let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...

In [7], Mozerov et al. propose to perform stereo matching as a twostep energy minimization problem. They formulate cost filtering as a local energy minimization model, and solve the fully connected MRF model and the locally connected MRF model sequentially. In this paper we intend to combine the two steps of energy minimization in order to improve stereo matching results. We propose to jointly ...

A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle S1 that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs. Furthermore, we show that such graphs are Hamilton-connected if and only if they are 3-...

A graph is locally connected if for each vertex v of degree --2, the subgraph induced by the vertices adjacent to v is connected . In this paper we establish a sharp threshold function for local connectivity . Specifically, if the probability of an edge of a labeled graph of order n is p = ((3/2 + s„) log n/n)'/ 2 where s„ _ ( log log n + log(3/8) + 2x)/(2 log n), then the limiting probability ...

Suppose that T is a spanning tree of a graph G. T is called a locally connected spanning tree of G if for every vertex of T , the set of all its neighbors in T induces a connected subgraph of G. In this paper, given an intersection model of a circulararc graph, an O(n)-time algorithm is proposed that can determine whether the circular-arc graph contains a locally connected spanning tree or not,...