We give a deterministic algorithm to find the minimum cut in a surface-embedded graph in near-linear time. Given an undirected graph embedded on an orientable surface of genus g,...
We clarify the computational complexity of planarity testing, by showing that planarity testing is hard for L, and lies in SL. This nearly settles the question, since it is widely...
It is shown that every planar graph with no separating triangles is a subgraph of a Hamiltonian planar graph; that is, Whitney’s theorem holds without the assumption of a triang...
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...
We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every...
Julian Yarkony, Alexander T. Ihler, Charless C. Fo...