For planar graphs, counting the number of perfect matchings (and hence determining whether there exists a perfect matching) can be done in NC [4, 10]. For planar bipartite graphs, ...
We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set pr...
We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-conn...
Glencora Borradaile, Erik D. Demaine, Siamak Tazar...
In John Tantalo’s on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by m...
To decide whether a line graph (hence a claw-free graph) of maximum degree five admits a stable cutset has been proven to be an NP-complete problem. The same result has been known...