# A First Course in Graph Theory and CombinatoricsPlanar Graphs

A First Course in Graph Theory and Combinatorics: Planar Graphs [A graph is said to be embedded in the plane if it can be drawn on the plane so that no two edges intersect. Such a graph is called a planar graph. Graphs arising from maps are clearly planar. In fact, planar maps can be characterized as such. Any planar map cuts out the plane into faces. To be precise, a maximal region of the plane which does not contain in its interior a vertex of the graph is called a face. A finite plane graph has also one unbounded face called the outer face. The faces are pairwise disjoint. The basic relation for planar graphs is the following theorem due to Euler.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A First Course in Graph Theory and CombinatoricsPlanar Graphs

Part of the Texts and Readings in Mathematics Book Series (volume 55)
Springer Journals — May 24, 2017
8 pages

/lp/springer-journals/a-first-course-in-graph-theory-and-combinatorics-planar-graphs-W3McyfKaQg
Publisher
Hindustan Book Agency
© Hindustan Book Agency (India) 2009
ISBN
978-81-85931-98-2
Pages
118 –126
DOI
10.1007/978-93-86279-39-2_10
Publisher site
See Chapter on Publisher Site

### Abstract

[A graph is said to be embedded in the plane if it can be drawn on the plane so that no two edges intersect. Such a graph is called a planar graph. Graphs arising from maps are clearly planar. In fact, planar maps can be characterized as such. Any planar map cuts out the plane into faces. To be precise, a maximal region of the plane which does not contain in its interior a vertex of the graph is called a face. A finite plane graph has also one unbounded face called the outer face. The faces are pairwise disjoint. The basic relation for planar graphs is the following theorem due to Euler.]

Published: May 24, 2017