The circumference of a graph with no K3,t-minor, II

  • Authors:

  • Guantao Chen;Xingxing Yu;Wenan Zang

  • Affiliations:

  • Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA and Faculty of Mathematics and Computer Science, Hubei University, Wuhan, China;School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA;Department of Mathematics, University of Hong Kong, Hong Kong, China

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

The class of graphs with no K"3","t-minors, t=3, contains all planar graphs and plays an important role in graph minor theory. In 1992, Seymour and Thomas conjectured the existence of a function @a(t)0 and a constant @b0, such that every 3-connected n-vertex graph with no K"3","t-minors, t=3, contains a cycle of length at least @a(t)n^@b. The purpose of this paper is to confirm this conjecture with @a(t)=(1/2)^t^(^t^-^1^) and @b=log"1"7"2"92.