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.

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...

Various methods of isolating cellulosic fibers from banana pseudo-stems including mechanical extraction, steam release, release combined with chemical treatment, and an enzymatic method pectinase Staphylococcus sciuri, were performed. The produced by all the characterized. In this work, we report on breaking tenacity, strength, fiber length, diameter, toughness, linear density enzyme-retted fib...

This paper describes an efficient algorithm to find a Hamiltonian circuit in an arbitrary 4-connected maximal planar graph. The algorithm is based on our simlplified version of Whitney's proof of his theorem: every 4-connected maximal planar graph has a Hamiltonian circuit.