In an earlier paper, we proved that an internally 4connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. We refine this result, by giving detailed descriptions of the operations required to produce the internally 4-connected minor. Each of these operations is top-down, in that it produces a smaller minor from ...

In this paper, we show that every 4-connected maximal plane graph with m finite faces other than the octahedron can be drawn in the plane so that at least (m+3)/2 faces are acute triangles. Moreover, this bound is sharp. © 2005 Published by Elsevier B.V.

It is shown that in a 4-connected maximal planar graph there is for any four vertices a, b, c and d, a cycle in the graph that contains the four vertices and visits them in the order a, b, c and d.

The concept of connectivity and its index have been widely discussed applied to environmental studies such as ecology, hydrology, geomorphology hydrosedimentology. Supposing that this is very useful also in disaster risk management, we define the hazard associated debris flows degree between flow occurrence (trajectory) point interest (location house, person, so on). Based on definition, Hazard...

high-density planting system is one of the effective methods for improving production and profitability of tree orchards. in this research, the effects of four planting densities (1904, 2666, 3137 and 4800 tree/ha) on annual shoot growth, tree yield, physicochemical properties of fruit and leaf mineral contents of apple (malus domestica borkh cv ‘granny smith’treegrafted on m26 clonal rootstock...

mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. a failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. a number of approaches have bee...