Abstract. The depth of a planar embedding is a measure of the topological nesting of the biconnected components of the graph. Minimizing the depth of planar embeddings has importan...
We prove a lower bound of (n4/3 log1/3 n) on the randomized decision tree complexity of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite g...
We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a lay...
Michael B. Dillencourt, David Eppstein, Daniel S. ...
Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easily can we decide whether it is possible to transform α into β by recolouring...
We characterize the finite graph algebras which are dualizable. Indeed, a finite graph algebra is dualizable if and only if each connected component of the underlying graph is eith...
Brian A. Davey, Pawel M. Idziak, William A. Lampe,...