Unavoidable Parallel Minors of 4-Connected Graphs

Details Unavoidable Parallel Minors of 4-Connected Graphs Unavoidable Parallel Minors of 4-Connected Graphs

2006-06-23

arxiv.org/abs/math/0606577v2

Mathematics

Combinatorics

12 pages, 3 figures

Scientific paper

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 Mobius zigzag ladder, the (2k)-rung zigzag ladder, or K_k. We also find the unavoidable parallel minors of 1-, 2-, and 3-connected graphs.

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