Saito, A linear 5-coloring algorithm of planar graphs
The central objects under study are planar graphs
and planar embedded graphs (also called maps).
We give the general form of the Tutte polynomial of a family of positive-signed connected planar graphs
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.
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
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
The max-flow and min-cut are also known to be equal or near-equal for certain special types of flows in planar graphs
(see Frank  and Schrijver  for a survey of such results).
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