Probabilistic Methods on Erdos Problems

On Induced Paths, Holes and Trees in Random Graphs

We study the concentration of the largest induced paths, trees and cycles (holes) in the Erdos-Renyi random graph model and prove a 2-point concentration for the size of the largest induced path and hole, for all p = Ω(n ln n). As a corollary, we obtain an improvement over a result of Erdos and Palka concerning the size of the largest induced tree in a random graph. Further, we study the path c...

On Some Problems of Bellman and a Theorem of Romanoff

The Strong Chromatic Index of Graphs

The strong chromatic index of graphs Mohammad Mahdian Master of Science Graduate Department of C o m p t e r Science University of Toronto 2000 A strong edge-colouring of a graph G is an assignrnent of colours to the edges of G such that every colour class is an induced matching. The minimum number of colours in such a colouring is called the strong chromatic index of G. In 1985, Erdos and Nese...

CBMS / NSF , Regional Research Conference in Mathematical Sciences : Probabilistic and Combinatorial Approach in Analysis

S OF THE TALKS Talks on August 6-10 August 6 Alex Iosevich, University of Missouri-Columbia. Analysis, combinatorics and number theory of the Mattila integral. Abstract: We shall discuss the Erdos/Falconer distance problem in discrete and continuous context, with Mattila integral playing a fundamental role. The role of number theory and combinatorics shall be emphasized throughout.

On the Irrationality of Certain Series

During my long life I have spent lots of time thinking about irrationality of series . The reader with a little maliciousness may say "spent and wasted" since I have never discovered any new general methods nor had any spectacular success like Apéry. Nevertheless I hope to convince the reader that not all of it was completely wasted . First of all, I state some of my previous results several of...