Planar graph algorithms constitute a pivotal area in theoretical computer science, addressing problems where graphs can be drawn on a plane without edge crossings. Among the myriad challenges in this ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

The weighted maximal planar graph (WMPG) is practically important in the laying out of facilities in modern manufacturing environments. Given a weighted complete graph, the WMPG seeks to find a ...

Data is presented on the number of 3-connected planar graphs, isomorphic to the graphs of convex polyhedra, with up to 26 edges. Results have been checked with the number of rooted c-nets of R. C.

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Let us say that a graph is k-apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex. It is ...