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Title: | Unavoidable parallel minors of 4-connected graphs |
Authors: | Chun, C Ding, G Oporowski, B Vertigan, D |
Issue Date: | 2009 |
Publisher: | Wiley Periodicals |
Citation: | Journal of Graph Theory, 60 (4): 313 - 326, Apr 2009 |
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 K_{4,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 K_k. We also find the unavoidable parallel minors of 1-, 2-, and 3-connected graphs. |
Description: | This is the post-print version of the Article - Copyright @ 2009 Wiley Periodicals |
URI: | http://onlinelibrary.wiley.com/doi/10.1002/jgt.20361/abstract?systemMessage=Wiley+Online+Library+will+be+disrupted+on+15+December+from+10%3A00-12%3A00+GMT+%2805%3A00-07%3A00+EST%29+for+essential+maintenance http://bura.brunel.ac.uk/handle/2438/7061 |
DOI: | http://dx.doi.org/10.1002/jgt.20361 |
ISSN: | 0364-9024 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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