The distinguishing number ∆(X) of a graph X is the least positive integer n for which there exists a function f : V (X) → {0, 1, 2, · · · , n−1} such that no nonidentity ...
We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system havi...
We show that the segment endpoint visibility graph of any finite set of disjoint line segments in the plane admits a simple Hamiltonian polygon, if not all segments are collinear. ...
In this paper we present the derivation details, logic, and motivation for the three loop calculus introduced in Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R)). Generating ...
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in ...