arXiv subjects
Publications and source records attributed to Peter Ulrickson.
We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for Mycielskians of important families of graphs, and construct families of graphs realizing particular values of (secure) domination parameters.
The well-known notion of domination in a graph abstracts the idea of protecting locations with guards. This paper introduces a new graph invariant, the autonomous domination number, which abstracts the idea of defending a collection of locations with autonomous agents following a simple protocol to coordinate their defense using only local information.
We construct spaces of 1-dimensional supersymmetric Euclidean field theories and show that they represent real or complex K-theory. A noteworthy feature of our bordism category is that the identity bordism of a point is connected to intervals of positive length.
We show that the only endofunctors of the category of quandles commuting with the forgetful functor to sets are the power operations. We also give a similar statement for racks.