Students who I have advised or am advising:
 Sam Donelley, Undergraduate honors thesis, 1997. `Powers of
Hamiltonian
paths and Powers of Hamiltonian Cycles in Threshold Graphs'. Now am
member of the Database Research Group, University of Pennsylvania.

Darren Narayan , PhD May 2000. `The Reversing Number of a
Digraph'. Now at Rochester Institute of Technology
 Trisha Moller, PhD August 2004. `tsplit interval orders'. Initially
at
DeSales University. Now working part time at Moravian College and part
time with family.
 Brian Heinold, PhD
May 2006. `Sum List Coloring and Choosability'. Now at Mt. St. Mary's
University Maryland.
 Jen
Scancella
Gorman, PhD August 2007, `Nested Traveling Salesperson
Problems', Now at Kutztown University.
 Ellen
Panofsky, PhD May 2008. `Graph Labeling Problems with Distance
Conditions', Now at Cabrini College.

Jonelle Hook, PhD May 2010. `The Clasisfication of Critical graphs
and StarCritical Ramsey Numbers', Now at Mt. St. Mary's University
Maryland.
 Breeanne Baker, Starting spring 2010.
 Kathleen Ryan, Starting Fall 2010.
 Aydin Gerek, Starting Spring 2011
 Matt Prudente, Starting fall 2011
Postdoctoral visitors to Lehigh that I have worked with:
 Art Busch
20052006, now at University of Dayton.
 Colton Magnant,
20082010,
now
at Georgia Southern University
Here are several unpublished papers:
 Examples of Combinatorial Duality : an
expository paper giving examples of the theorem of the alternative for
linear
inequalities is used to prove Hoffman's circulation theorem and then
from this Fishburn's Interval order representation
theorem and Landau's theorem for score sequences of tournaments.
 Chain Packings and Odd Subtree Packings :
an old unpublished paper building on work from my PhD thesis. It seems
that part of what I did had been done before and the other part done
several years later by others.
Here are slides from some talks:
 Perfect maps and factors : My first
computer
based talk.
 When does x < a, x > 0 have a solution?
:
A talk for undergraduates based on my expository paper `Examples
of combinatorial duality'.
 Score sequences for
tournaments
Another talk for undergraduates
 An edge Count Criterion for
Degree
Sequences On degree sequences for edge colored graphs
 Intervals and orders: what comes after
interval orders
A talk for a special session in memory of Ken Bogart
 Distinguishing number of
cartersian
products of complete graphs
 Structure of bipartite probe interval graphs
 Star avoiding Ramsey numbers
 Score sequences for
tournaments
Another talk for undergraduates
This is an out of date description. The
papers also
are linked
in
the list above.
A research statement from my tenure file in 1998
Here are some of my current research interests and favorite problems. Well  not really; my favorite problems are the hard well known ones. I will mention problems that are less well known and closely related to my current research
Feedback Arc Digraphs: who gets upset in tournament rankings
A feedback arc set in a digraph is a set of arcs whose removal makes the digraph acyclic. A minimum size feedback arc set in a tournament is also the set of arc inconsistent with a `ranking' which minimizes inconsistencies. Every acyclic digraph is a feedback arc set of some tournament. That is, given an acyclic digraph, which we think of as the inconsistencies from a ranking, what is the smallest size of a tournament in which the ranking procedure described above gives exactly those inconsistencies. (We do allow a ranking procedure to produce several equal rankings and we search for the inconsistencies under one of these.) In particular we can look at `the' acyclic tournament as the set of inconsistencies. This provides bounds for other acyclic digraphs. So we ask: what is the smallest size of a tournament which produces a set of n people each pair of which is ranked wrong. I have a specific conjecture about this, along with partial results and related questions in Tournaments as Feedback Arc Sets (Electronic Journal Of Combinatorics Vol 2 (1995) article R20). The partial results are obtained by viewing the problem as an integer linear programming problem. More recent results have been obtained with recent Lehigh PhD Darren Narayan. See his research page for more information.
Powers of Hamiltonian Paths
Label the vertices of a graph so as to maximize the minimum distance between nonadjacent vertices. This is in a sense dual' to the bandwidth problem, which seeks to minimize the maximum distance between adjacent vertices. This problem is also a variant on Hamitonian paths, looking for powers of Hamiltonian paths instead. Some of my papers on this are: Hamiltonian Powers in Threshold and Arborescent Comparability Graphs (with Sam Donnelly, Discrete Mathematics 202 (1999) 3344) and Powers of Hamiltonian Paths in Interval Graphs (Journal of Graph Theory 28 (1998) 3138).
Perfect Maps: how determine your location in n dimensions
List the string 00011101 cyclically. Each triple occurs exactly once. This is known as a perfect map or de Bruijn cycle. Many questions can be asked about higher dimensional versions of this and version with an alphabet of size k (instead of 2). In particular are the `obvious' necessary conditions sufficient? Kenny Patterson in London has answered this completely in 2dimensions for k a prime power. Many other interesting questions arise about related structures called perfect factors and perfect multifactors which arise in the study of these objects. For more information and references to other work see these papers my recent paper (which is partially survey and partially new unifying results and notation Constructing Higher Dimensional Perfect Factors (to appear in Aequationes Mathematicae)
Some recent work on the Prague dimension (product dimension) of graphs with a suprising connection to orthogonal latin squares can be found in Representations of graphs modulo n (with Anthony Evans and Darren Narayan, Discrete Mathematics 223 (2000) 109123)