Given a family \(\mathcal G\) of graphs on common vertex set X, we say that is rainbow connected if for every pair \(u,v \in X\), there exists path from u to v uses at most one edge each graph G\). We consider the case contains s graphs, sampled randomly G(n, p), with \(n = |X|\) and \(p \frac{c \log n}{sn}\), where \(c > 1\) constant. show threshold three consecutive integer values such when g...

Gradient methods subject images to a series of operations enhance some characteristics and facilitate image analysis, usually the contours large objects. We argue that gradient must show other characteristics, such as minor components uniform regions, particularly for segmentation task where subjective concepts region coherence similarity are hard interpret from pixel information. This work ext...