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Removable edges in a cycle of a 4-connected graph
- Source :
-
Discrete Mathematics . Oct2004, Vol. 287 Issue 1-3, p103-111. 9p. - Publication Year :
- 2004
-
Abstract
- Abstract: Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting in the graph ; second, for all the vertices x of degree 3 in , delete x from and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by . If is still 4-connected, then e is called a removable edge of G. In this paper, we investigate the problem on how many removable edges there are in a cycle of a 4-connected graph, and give examples to show that our results are in some sense the best possible. [Copyright &y& Elsevier]
- Subjects :
- *GRAPH theory
*COMBINATORICS
*PLANE geometry
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 287
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 19295501
- Full Text :
- https://doi.org/10.1016/j.disc.2004.05.015