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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
ISSN: 0364-9024
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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