dimensions_id
pub.1025594661
Mathematical Sciences
1989-03-01
false
Boolean approach to planar embeddings of a graph
research_article
en
64-79
2019-04-11T12:03
https://scigraph.springernature.com/explorer/license/
The purpose of this paper which is a sequel of “ Boolean planarity characterization of graphs ” [9] is to show the following results.Both of the problems of testing the planarity of graphs and embedding a planar graph into the plane are equivalent to finding a spanning tree in another graph whose order and size are bounded by a linear function of the order and the size of the original graph, respectively.The number of topologically non-equivalent planar embeddings of a Hamiltonian planar graphG is τ(G)=2c(H)−1, wherec (H) is the number of the components of the graphH which is related toG. Both of the problems of testing the planarity of graphs and embedding a planar graph into the plane are equivalent to finding a spanning tree in another graph whose order and size are bounded by a linear function of the order and the size of the original graph, respectively. The number of topologically non-equivalent planar embeddings of a Hamiltonian planar graphG is τ(G)=2c(H)−1, wherec (H) is the number of the components of the graphH which is related toG.
http://link.springer.com/10.1007/BF02107624
articles
1989-03
79ef771a587009caaa0886d09bd1cee319767727af11443df6a5c391f8223ed8
readcube_id
Springer Nature - SN SciGraph project
1439-7617
Acta Mathematica Sinica, English Series
1439-8516
Pure Mathematics
10.1007/bf02107624
doi
5
Liu
Yanpei
Rutgers University
RUTCOR, Rutgers University, USA
1