My research interests lie in Graph Theory and Combinatorics. As is
well-known, Graph Theory is growing into a wide-ranged topic in
mathematical sciences. The graph itself is a fundamental figure
consisting of points (vertices) and lines (edges). Because of its
simple character, it has wide applicability.
I received the degree of Ph.D. from the University of Tokyo in 1989.
In my doctoral thesis, I studied the connectivity of graphs.
Connectivity is one of the best indicators for the reliability of a
network. In a pure graph-theoretical sense, graphs with high
connectivity contain a wealth of subgraph structures, as seen in
Menger's theorem which says that any two vertices in an
n-connected graph are joined by n internally disjoint
paths, and Dirac's theorem which says that any n-vertices in an
n-connected graph lie on a common cycle. My current interest
in Graph Theory is to discover basic properties of n-connected
graphs.
One of the most interesting problems is to find a generation theorem
of n-connected graphs. The aim of generation theorem is
to recognize the set of n-connected graphs in terms of some
"base" graphs and constructing procedures. In the case where n ¡æ 5,
this problem is still open. The inverse of a constructing procedure is
a reduction procedure which preserves the given connectivity.
Edge-relation and edge-contraction are the most fundamental of these.
One of the main results of my doctoral thesis is concerning these
reduction procedures of n-connected graphs.
Because there are many unsolved problems in Graph Theory and
Combinatorics, my research interests extend over all the combinatorial
problems.