Portland Area Lecture Series

Of

Graph Theory and Combinatorics

2008-09 SCHEDULE

Weds, October 22 – Chuck Dunn 

(Linfield College)

"Game Coloring with Trees and Forests"

7:00pm, Room 381, Neuberger Hall

Abstract: We will consider the following game.  Two players, Alice and Bob,
alternate coloring the uncolored vertices of a finite graph G from a set
of r colors X.  At every step, adjacent vertices must receive different
colors.  Alice wants to ensure that all vertices are eventually colored,
while Bob wants to force a situation where there is an uncolored vertex
which cannot be colored.  The least r such that Alice has a winning
strategy is called the game chromatic number of G.  We will
consider this game on trees and forests and find the smallest tree

With maximum game chromatic number for trees.

Weds, November 19 – Josh Laison

(Willamette University)

" Obstacle Numbers of Graphs"

7:00pm, Room 381, Neuberger Hall

Abstract: This talk will be about work done this past summer with two students in
the Willamette Valley REU-RET project.  An obstacle representation of a
graph G is a drawing of G in the plane with straight line edges, together
with a set of polygons called obstacles, such that an edge exists in G if
and only if it does not intersect an obstacle.  The obstacle number of G
is the smallest number of obstacles in any obstacle representation of G.
Previous research about obstacle numbers seemed to suggest that most, if
not all, graphs had obstacle number 1.  In this talk we'll show that there
exist graphs with arbitrarily large obstacle number.  On the other hand,
most of the graphs we know still have obstacle number 1, and there are a
large number of questions still open.

Weds, February 4 – Robert Bailey

(Carleton University)

"Packing spanning trees in graphs and bases in matroids"

7:00pm, Room 222, Neuberger Hall

Abstract: The spanning tree packing number of a graph G, denoted 

σ(G), is the largest number of edge-disjoint spanning trees in G. An 

obvious upper bound on σ(G) is the edge-connectivity of G. We 

consider those graphs for which these two parameters are equal, and obtain 

a constructive description of them. We can also ask an equivalent question 

for matroids, and will conclude by mentioning this.

This is joint work with Brett Stevens (Carleton)

and Mike Newman (Ottawa).

Weds, February 25 – Mike Rowell

(Pacific University)

"Partition Theory and the Lebesgue Identity"

7:00pm, Room 222, Neuberger Hall

Abstract: A crash course in partition theory and common methods will

be given.   We will then introduce a new combinatorial proof of the

Lebesgue identity using our new found knowledge and discuss how this

leads to a new finite form of the identity.  Using this new finite

form we are able to make new observations about special cases of the

Lebesgue identity, namely the "little" Goellnitz theorems and

Sylvester's identity.

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