https://www.um.edu.mt/library/oar/handle/123456789/23634 2026-04-14T11:17:14Z https://www.um.edu.mt/library/oar/handle/123456789/24489 Title: The Collection V Editors: Sciriha, Irene; Telenta, Tanya Abstract: Fifth issue of The Collection, a journal by the Department of Mathematics at the University of Malta. 2002-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24472 Title: New necessary and sufficient conditions for the Zarankiewicz conjecture on crossing numbers Abstract: The purpose of this presentation is to give a historical outline about the theory of crossing numbers, and to present the current status of long standing problems on crossing numbers of complete bipartite graphs. A set of new necessary and sufficient conditions are given for the Zarankiewicz conjecture on the crossing number of complete bipartite graphs. These conditions are expressed in terms of the crossing numbers' divisibility properties and their expressibility as polynomials. 2002-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24461 Title: Boolean matrices Abstract: In this short note, we will use Boolean matrices to help us find some interesting graph theoretical properties regarding the distance and index of a graph. First we will give some definitions that are necessary for the theorems which follow. 2002-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/24444 Title: A new form of primes Abstract: Let P1, P2, ...., Pk,... denotes the ordered sequence of primes. We will consider primes of the form p=1modpi. Moreover we give a new proof to the converse W. Isean's Theorem, first proved by Lagrange. 2002-01-01T00:00:00Z