Abstract. We present an expected polynomial time algorithm to generate a labeled planar graph uniformly at random. To generate the planar graphs, we derive recurrence formulas that...
Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the ...
Minor containment is a fundamental problem in Algorithmic Graph Theory, as numerous graph algorithms use it as a subroutine. A model of a graph H in a graph G is a set of disjoint ...
Isolde Adler, Frederic Dorn, Fedor V. Fomin, Ignas...
We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
We present a reduction method that reduces a graph to a smaller core graph which behaves invariant with respect to planarity measures like crossing number, skewness, and thickness....