A copy of the thesis will be available for viewing in the General Office of the
Department of Mathematics and Statistics SSM A425 at least one week prior to the
oral examination.

Abstract and announcement (pdf file)

A copy of his Dissertation is available for perusal in SSM A425.

A copy of the thesis will be available for viewing in the General Office of the Department of Mathematics and Statistics at least one week prior to the oral examination.

Announcement and abstract (PDF file)

Abstract

An edge ordering of a graph G = (V,E) is an injection f : E → R, where R denotes the set of real numbers. A path in G for which the edge ordering f increases along its edge sequence is called an f-ascent; an f-ascent is maximal if it is not contained in a longer f -ascent. The depression of G is the smallest integer k such that any edge ordering f has a maximal f -ascent of length at most k. In this dissertation we discuss various results relating to the depression of a graph. We determine a formula for the depression of the class of trees known as double spiders. A k-kernel of a graph G is a set of vertices U⊆V(G) such that for any edge ordering f of G there exists a maximal f -ascent of length at most k which neither starts nor ends in U. We study the concept of k-kernels and discuss related depression results, including an improved upper bound for the depression of trees. We include a characterization of the class of graphs with depression three and without adjacent vertices of degree three or higher, and also construct a large class of graphs with depression three which contains graphs with adjacent vertices of high degree. Lastly, we apply the concept of ascents to edge colourings using possibly fewer than ∥E(G)∥ colours (integers). We consider the problem of determining the minimum number of colours for which there exists an edge colouring such that the length of a shortest maximal path of edges with increasing colors has a given length.

Program of the Final Oral Examination for the Degree of Master of Science

DEPARTMENT OF MATHEMATICS AND STATISTICS of
VERONICA SABELNYKOVA

“Bayesian Methods for Joint Modeling of Survival and Longitudinal Data: Applications and Computing”

Monday, December 10, 2012 2:00pm David Strong Building, room C108

A copy of the thesis will be available for viewing in the General Office of the Department of Mathematics and Statistics at least one week prior to the oral examination.

Dr. David Capson Dean, Faculty of Graduate Studies

Priya Grewal is presenting her STATS Project (Non-Thesis Oral Exam) on Monday, December 10th @ 11 am.