Eugene Lee (Carnegie Mellon): Catching an invisible intruder on subdivisions of a graph

We wish to locate an intruder who is hiding at one of the
vertices of a graph G. At each step, we are allowed to ‘check’an
arbitrary set of k vertices. If the intruder is presently at any of
those vertices, then we win. Otherwise, the intruder may choose to move
to an adjacent vertex or remain in place. The intruder is ‘invisible’:
we have no way of knowing if or where the intruder moves. We call the
smallest k such that we can guarantee the capture of the intruder
after finitely many steps the search number of G. In this talk I will
describe some results and problems around the search number, with a
particular emphasis on its behavior under edge-subdivisions. This is a
joint work with Anton Bernshteyn (Georgia Tech).