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#### Rings, Group Rings, and Their Graphs

(Brock University, 2013-09-05)

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. ...

#### Edge-choosability of Planar Graphs

(Brock University, 2013-09-26)

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s ...

#### Zero-sum problems in finite cyclic groups

(Brock University, 2009-01-28)

The purpose of this thesis is to investigate some open problems in the area of
combinatorial number theory referred to as zero-sum theory. A zero-sequence in a
finite cyclic group G is said to have the basic property if ...

#### Response curves of deterministic and probabilistic cellular automata in one and two dimensions

(2012-04-02)

One of the most important problems in the theory of cellular automata (CA) is
determining the proportion of cells in a specific state after a given number of time
iterations. We approach this problem using patterns in ...

#### Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

(Brock University, 2013-09-05)

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph ...

#### The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

(2012-03-30)

This work consists of a theoretical part and an experimental one. The first part
provides a simple treatment of the celebrated von Neumann minimax theorem as
formulated by Nikaid6 and Sion. It also discusses its relationships ...