A simple geometrical proof is given in order to show that any two maximally entangled states of three spin–1/2 particles are locally unitarily connected. And assuming a condition, which ensures that a typical plane in a Hilbert space of n spin–1/2 particles contains at least one product state, it is shown that any two maximally entangled states of spin–1/2 particles are locally unitarily connec...

Text localization from scene images is a challenging task that finds application in many areas. In this work, we propose a novel hybrid text localization approach that exploits Multi-resolution Maximally Stable Extremal Regions to discard false-positive detections from the text confidence maps generated by a Fast Feature Pyramid based sliding window classifier. The use of a multi-scale approach...

For a non-trivial connected graph G, a set S ⊆ V (G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum order of its edge geodetic sets and any edge geodetic set of order g1(G) is an edge geodetic basis. A connected edge geodetic set of G is an edge geodetic set S such that the ...

For a non-trivial connected graph G, a set S ⊆ V (G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum order of its edge geodetic sets and any edge geodetic set of order g1(G) is an edge geodetic basis. A connected edge geodetic set of G is an edge geodetic set S such that the ...

The relationship between graph coloring and the immersion order is considered. Vertex connectivity, edge connectivity and related issues are explored. It is shown that a t-chromatic graph G contains either an immersed Kt or an immersed t-chromatic subgraph that is both 4-vertex-connected and t-edge-connected. This gives supporting evidence of our conjecture that if G requires at least t colors,...