## Staff -TANIGAWA, Shinichi-

Name

**TANIGAWA, Shinichi**
Position
Assistant Professor

E-Mail
tanigawa (email address: add @kurims.kyoto-u.ac.jp)

Research

My general research interests lies in the interface between
combinatorial optimization and discrete mathematics. Within these
general areas, I have focused on rigidity theory, in particular, on
the combinatorial aspect of graph rigidity. The central topic in
rigidity theory is the rigidity of graphs (or linkages), which
concerns with the local or global uniqueness of realizations of graphs
in Euclidean space with given edge lengths. By Asimov-Roth (1978) for
local rigidity and by Gortler-Healy-Thurston (2010) for global
rigidity, it was shown that the rigidity property is invariant among
generic realizations and thus a property of graphs. Laman's landmark
result from 1970 implies that Maxwell's necessary condition is
sufficient for graphs realized generically in 2-space, implying a
combinatorial characterization of rigid graphs in 2-space. However,
for higher dimensional space, Maxwell's condition is no longer
sufficient, and establishing the corresponding result in 3-space is
recognized as one of the most important open problems in this field.
Similarly, for global rigidity, the solution of Connelly's conjecture
by Jackson and Jordan (2005) implies a combinatorial characterization
of globally rigid graphs in 2-space, and the problem is open for
higher dimension. Toward solving the problem of characterizing
locally/globally rigid graphs in 3-space, I have proposed several new
approaches and established partial results. I am also interested in
extending the theory to non-generic situations for which the existing
theory for generic realizations cannot be applied.
Recently I am also working on combinatorial optimization problems
related to submodular functions.