Unavoidable parallel minors of 4-connected graphs

  • Authors:

  • Carolyn Chun;Guoli Ding;Bogdan Oporowski;Dirk Vertigan

  • Affiliations:

  • Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana;Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana;Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana;Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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