Research interests: Daniel
Ullman
The word ``graph'' when used
in the phrase ``graph theory'' refers to a set of vertices with various
pairs of vertices connected by edges. Some call such things ``networks''.
The discipline dates back to 1736, the year that Euler presented his famous
puzzle about the seven bridges of Königsberg. The discipline, however,
is quite modern, and has flourished in the past two decades. Today, there
are numerous connections to algebra, analysis, and topology, in addition
to links with computer science, logic, probability theory, and operations
research. My special areas of interest within graph theory include the
study of fractional analogues of integer-valued graph invariants, the interaction
between combinatorial game theory and graphs, the representation of graphs
by geometric objects, the chromatic theory of graphs (i.e., graph coloring),
and the computational complexity of various graph problems.
Selected Publications
-
On tensor powers of integer
programs, SIAM J. Disc. Math. 5 (1992) 127-143 (with R. Pemantle,
J. Propp).
-
Sequential compounds of combinatorial
games, J. Theor. Comp. Sci. 119, (1993) 311-321 (with W. Stromquist).
-
Fractional isomorphism of
graphs, J. Graph Theory 132 (1994) 247-265 (with M. Ramana, E. Scheinerman).
-
The fractional chromatic
number of Mycielski's graphs, J. Graph Theory
19 (1995) 411-416
(with J. Propp, M. Larsen).
-
On point-hyperspace graphs,
J. Graph Theory 20 (1995) 19-35 (with E. Scheinerman, A. Trenk).