The bandwidth minimization problem has a long history and a number of practical applications. In this paper we introduce a natural extension of bandwidth to partially ordered layo...
Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the noti...
We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the mon...
Given an edge-weighted graph where all weights are nonnegative reals, an edge reweighting is an assignment of nonnegative reals to edges such that, for each vertex, the sums of giv...
We study the properties of affine rigidity of a (hyper)graph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., only depen...
Steven J. Gortler, Craig Gotsman, Ligang Liu, Dyla...