Name
Abstract | ||
|---|---|---|
A parallel minor is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer k, every internally 4-connected graph of sufficiently high order contains a parallel minor isomorphic to a variation of K4,k with a complete graph on the vertices of degree k, the k-partition triple fan with a complete graph on the vertices of degree k, the k-spoke double wheel, the k-spoke double wheel with axle, the (2k+1)-rung Möbius zigzag ladder, the (2k)-rung zigzag ladder, or Kk. We also find the unavoidable parallel minors of 1-, 2-, and 3-connected graphs. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 313-326, 2009 |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1002/jgt.v60:4 | Journal of Graph Theory |
Keywords | Field | DocType |
parallel minor,complete graph,3-connected graph,k-spoke double wheel,parallel minor isomorphic,degree k,unavoidable parallel minor,parallel edge deletion,4-connected graph,positive integer k,connected graph | Wheel graph,Discrete mathematics,Topology,Complete graph,Combinatorics,Wagner graph,Cycle graph,Distance-regular graph,Graph minor,Symmetric graph,Petersen graph,Mathematics | Journal |
Volume | Issue | ISSN |
60 | 4 | 0364-9024 |
Citations | PageRank | References |
3 | 0.50 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carolyn Chun | 1 | 25 | 8.25 |
| Guoli Ding | 2 | 444 | 51.58 |
| Bogdan Oporowski | 3 | 266 | 23.24 |
| Dirk Vertigan | 4 | 331 | 32.14 |