References in periodicals archive ?
The collaborative effort of six editors, "Current Developments in Mathematics: 2011" is comprised of three major articles focusing on advanced mathematics: 'The Laplacian on planar graphs and graphs on surfaces' by R.
This includes the class of forests, series-parallel graphs, planar graphs, and many more.
In the first part, he explains trees and bipartite graphs, chordal graphs, planar graphs, graph coloring, and traversals and flows.
We will combine planar graphs of the solids with their duals in a special way to obtain our PELARGONIUMS.
Yannakakis has investigated the book embedding problem for planar graphs, showing that four pages are sufficient to book embed a planar graph [12].
Some key mathematical concepts that we will use are abstract graphs, graph drawing, planar graphs, and plane graphs.
Covering planar graphs with forests, Journal of Combinatorial Theory, Series B, Vol.
Riskin asked if his result holds for arbitrary 3-connected planar graphs.
We show that the maximum nonoverlapping dense blocks problem is NP-complete by a reduction from the maximum independent set problem on cubic planar graphs.
Conversely -- as he notes in a paper to be published in the proceedings of the Second International Meeting of Origami Science and Scientific Origami, held last November in Otsu, Japan -- origami has served as a source of ideas for his own mathematical research on planar graphs.
The generating functions B(z), C(z), D(z), S(z), P(z) and H(z) correspond to distinct families of edge-rooted cubic planar graphs, and u(z) is an algebraic function related to the enumeration of 3-connected cubic planar graphs (dually, 3-connected triangulations).
Except of these results we currently have only very sparse information about how the evolution of a random planar graph does look like, and how random planar graphs with fixed average degree typically behave.