Topological minors in line graphs — A proof of Zha’s conjecture

Abstract

In 1992, Xiaoya Zha conjectured that the line graph of a 3-connected non-planar graph contains a subdivision of K 5. In this paper we prove this conjecture. This result is the main ingredient of [4] where a complete characterization of all the 4-connected claw-free graphs not containing a subdivision of K 5 is obtained.

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Correspondence to Roi Krakovski.

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Krakovski, R. Topological minors in line graphs — A proof of Zha’s conjecture. Combinatorica 34, 207–252 (2014). https://doi.org/10.1007/s00493-014-2721-3

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Mathematics Subject Classification (2000)

  • 05C83
  • 05C76
  • 05C38