We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter tM(I) is defined as the infimum of all such supremums. We show that if I has length 1, then tM(I) = 1 2 . We make three general conjectures relating to the value of tM(I) for intervals I of length less than 4. We also con...

22 From the rst and third, we get

This document describes Diameter applications that are used for Authentication, Authorization and Accounting (AAA) in the Network Access Server (NAS) environment. This application, combined with the Diameter base protocol, Transport Profile, EAP and CMS Security specifications, satisfies typical network access services requirements. Initial deployments of the Diameter protocol are expected to i...

Given a configuration of indistinguishable pebbles on the vertices of a connected graph G on n vertices, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one pebble on an adjacent vertex. The m-pebbling number of a graph G, πm(G), is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of p...

A graph that contains a spanning tree of diameter at most t clearly admits a tree t-spanner, since a tree t-spanner of a graph G is a sub tree of G such that the distance between pairs of vertices in the tree is at most t times their distance in G. In this paper, graphs that admit a tree t-spanner of diameter at most t + 1 are studied. For t equal to 1 or 2 the problem has been solved. For t = ...

The EAP Re-authentication Protocol (ERP) defines extensions to the Extensible Authentication Protocol (EAP) to support efficient re-authentication between the peer and an EAP Re-authentication (ER) server through a compatible authenticator. This document specifies Diameter support for ERP. It defines a new Diameter ERP application to transport ERP messages between an ER authenticator and the ER...

We prove that for every connected 4-colourable graph G of order n and minimum degree δ ≥ 1, diam(G) ≤ 5n 2δ − 1. This is a first step toward proving a conjecture of Erdős, Pach, Pollack and Tuza [4] from 1989.

Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...

Diameter of the 2 k-node Knn odel graph is d(k + 2)=2e:

For a pair of positive parameters D,χ, a partition P of the vertex set V of an n-vertex graph G = (V,E) into disjoint clusters of diameter at most D each is called a (D,χ) network decomposition, if the supergraph G(P), obtained by contracting each of the clusters of P , can be properly χ-colored. The decompositionP is said to be strong (resp., weak) if each of the clusters has strong (resp., we...