We investigate in this paper the computational complexity of the problem of determining if a graph has a 2-role assignment with two different roles.Expand

A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals overlap and at least one of them is a Probe.Expand

Role assignments, introduced by Everett and Borgatti [2], who called them role colorings, formalize the idea, arising In the theory of social networks, that individuals of the same social role will… Expand

In this paper we consider the "average-case" performance of two closely related versions of Rule k for the model of random unit disk graphs constructed from n random points in an $\ell_n\times \ell_N$ square.Expand

Let D be the punctured unit disk. It is easy to see that no pair x, y in D can cover D in the sense that D cannot be contained in the union of the unit disks centred at x and y. With this fact in… Expand