![](/images/graphics-bg.png)
Graphs with no K3,3 Minor Containing a Fixed Edge
Author
Source
International Journal of Combinatorics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-20
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
It is well known that every cycle of a graph must intersect every cut in an even number of edges.
For planar graphs, Ford and Fulkerson proved that, for any edge e, there exists a cycle containing e that intersects every minimal cut containing e in exactly two edges.
The main result of this paper generalizes this result to any nonplanar graph G provided G does not have a K3,3 minor containing the given edge e.
Ford and Fulkerson used their result to provide an efficient algorithm for solving the maximum-flow problem on planar graphs.
As a corollary to the main result of this paper, it is shown that the Ford-Fulkerson algorithm naturally extends to this more general class of graphs.
American Psychological Association (APA)
Wagner, Donald K.. 2013. Graphs with no K3,3 Minor Containing a Fixed Edge. International Journal of Combinatorics،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-497747
Modern Language Association (MLA)
Wagner, Donald K.. Graphs with no K3,3 Minor Containing a Fixed Edge. International Journal of Combinatorics No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-497747
American Medical Association (AMA)
Wagner, Donald K.. Graphs with no K3,3 Minor Containing a Fixed Edge. International Journal of Combinatorics. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-497747
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-497747