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SIAMDM
2008
13 years 7 months ago
2008
We prove a conjecture of Erdos, Purdy, and Straus on the number of distinct areas of triangles determined by a set of n points in the plane. We show that if P is a set of n points...
SIAMDM
2008
13 years 7 months ago
2008
Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n +I denote Kn,n with a 1-factor added. It is proved in this paper that there exists an m-c...
SIAMDM
2008
13 years 7 months ago
2008
For a rooted graph G, let EV (G; p) be the expected number of vertices reachable from the root when each edge has an independent probability p of operating successfully. We examine...
SIAMDM
2008
13 years 7 months ago
2008
We establish new lower and upper bounds for the real number graph labelling problem. As an application, we completely determine the optimum spans of L(p, q)-labellings of the infin...
SIAMDM
2008
13 years 7 months ago
2008
A classical theorem by Tutte assures the existence of a Hamilton cycle in every finite 4-connected planar graph. Extensions of this result to infinite graphs require a suitable co...