We show that the mistake bound for predicting the nodes of an arbitrary weighted graph is characterized (up to logarithmic factors) by the cutsize of a random spanning tree of the...
A nonplanar graph G is near-planar if it contains an edge e such that G−e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from diffe...
We consider a graph with n vertices, and p < n pebbles of m colors. A pebble move consists of transferring a pebble from its current host vertex to an adjacent unoccupied verte...
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...