Each
participant in our program produces a paper describing their results. As
the program is only eight weeks long, participants don't have much time to
revise and polish their papers. When viewing the papers below, please keep
in mind that they are not intended to be final versions, but are works in
progress. The students have worked hard to produce these results, and
have done a great job! The research represented by these papers was made
possible by NSF-REU grants DMS-9987955, DMS-0139426, and DMS-0453605, as well
as the generous support of
Some of our students have
worked in combinatorics, on graph labeling problems.
To see papers in combinatorics, click on one of
the names below.
Summer 2007 Combinatorics
Projects
Tree Congestion for Complete n-Partite Graphs, by Allen
Cox
Spanning Tree Congestion Critical Graphs, by Daniel
Tanner
On Spanning Tree Congestion of Product Graphs, by Rachel
Hunter
On 3-cyclic Cutwidth
Critical Graphs, by Matthew Straughn
On 3-cyclic Bandwidth Critical Graphs, by Eric Bucher
Summer 2006 Combinatorics
Projects
Two-Dimensional Bandwidth, by Chris
Duran
Edge Bandwidth,
by Taijiro
Bernstein
3 and 4-Bandwidth Critical Graphs, by Ann
Kilzer
Investigation of 4-Cutwidth Critical Tree Graphs and
Complete Cyclic Cutwidth Critical Graphs, by Ruffin
Swain
Summer 2005 Combinatorics
Projects
The Tree Congestion of Graphs, by Diana
Carr
On the Cyclic Cutwidth of
Complete Tripartite and n-Partite Graphs,
by Heather Allmond
On 3-bandwidth Critical Graphs, by Holly Westerfield
The Linear Cutwidth of
Complete n-Partite Graphs, by Chelsea Weitzel
Summer 2004 Combinatorics
Projects
The Linear Cutwidth of Complete
Bipartite and Tripartite Graphs, by Stephanie Bowles
The Linear and Cyclic Wirelength
of Complete Bipartite Graphs, by Liz Hartung
On Tree Congestion of Graphs, by Stephen
Hruska
Minimum Grid Cutwidth of
Complete Bipartite Graphs, by Karl Quick
Summer 2003 Combinatorics Projects
The Cyclic Cutwidth of Qn, by Jason Erbele
A Proof for the Cyclic Cutwidth
of Q6, by Candi Castillo
The Embedding of Complete Bipartite Graphs onto 2´n Grids with Minimum Grid Cutwidth, by
Carlos Ibarra
The Cyclic Cutwidth of
Complete Bipartite Graphs, by Megan Holben
Summer 2002 Combinatorics
Projects
On Which Graphs Have Linear Cutwidth Equal to Cyclic Cutwidth, by Melissa Banister
The Linear and Cyclic Cutwidth of the Complete
Bipartite Graph, by Matt Johnson
Cutwidth of a Complete Graph embedded on an
m × n Grid, by Brad Marchand
Proof of the Grid Cutwidth for a Complete Graph,
by Alvin Sacdalan
The Cyclic Cutwidth of a P2 × P2 × P n Mesh, by Victor Sciortino
Summer 2001 Combinatorics Projects
A Proof for the Cyclic Cutwidth of Q5, by
Ryan Aschenbrenner
Bandwidths, Cutwidths, and Wirelengths
of Complete Graphs of triangular and related numbers embedded on triangular
lattice grid host graphs, by LeeAnn Feathers
The cutwidth of the complete graph on 2n vertices
when embedded into a 2×n grid, by Annie Wang
Other students have worked with knot theory. Below are some of their
papers.
Summer 2007 Knot Theory Projects
Convexity and Minimum Distance Energy, by Rosanna
Speller
Ropelength of Braids and Tangle Decomposition of Knots, by Sarah
Ruether
On Ropelength of Alternating Links, by Shahla
Sadjadi
Summer 2006 Knot Theory Projects
The Crossing Probability Knot Energy, by Blake
Mitchell
Upper Bound for Ropelength of Pretzel Knots, by Safiya Moran
The Minimum Distance Energy and Midpoint Insertion, by Stephanie
Proksch
The Minimum Distance Energy for Polygonal Unknots, by Johanna
Tam
Summer 2005 Knot Theory Projects
The Twist Numbers of Graphs and the Tutte Polynomial,
by Thomas Albertson
An Upper Bound on Stick Numbers for Links, by Erik
Insko
On the Second Twist Number, by Gabriel
Murillo
Twist Numbers of Links from the Jones Polynomial, by Matthew
Williamson
Summer 2004 Knot Theory Projects
The Twisted Torus and Knots, by Jenny
Buontempo
The Supercrossing Index of Torus Knots, by Ryan Petitfils
Knotted Ribbons and Ribbon Length, by Maria
Salcedo
The Stick Number of Tr,4r, by Ivan
Ventura
Summer 2003 Knot Theory
Projects
Star Move and Construction of a
10-Stick 11-Crossing Knot, by Naomi Davis
The n-iterated Clasp Move and Torus Links, by Stacy Nicole Mills
Iterated Clasp Move and Upper Bounds for 2-bridge Links, by Tim Nawojski
Self-Linking Number as a Geometric Invariant through
Geo(8), by Joseph Rhoads
Summer 2002 Knot Theory Projects
On the Lower Bounds of Ramsey Numbers of Knots, by Joe
Clark
Knots in a Cubic Lattice, by Marta Kobiela
Stick Numbers of Links with Two Trivial Components, by Alexa Mater
Summer 2001 Knot Theory Projects
Clasping Within Polygonal Links, by Adam O'Connor
Minimum Stick Number for Knots and Links, by Bart Podlesny
Upper Bounds for the Stick Number of Three-Braids, by Nerissa Soriano
Upper Bounds for the Stick Numbers of Three Braids, by Diana Wall