A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains o...
Bastian Katz, Marcus Krug, Ignaz Rutter, Alexander...
Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partit...
We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, ...