Topological minors in line graphs - A proof of Zha's conjecture

Roi Krakovski

doi:10.1007/s00493-014-2721-3

Topological minors in line graphs - A proof of Zha's conjecture

Roi Krakovski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	207-252
Number of pages	46
Journal	Combinatorica
Volume	34
Issue number	2
DOIs	https://doi.org/10.1007/s00493-014-2721-3
State	Published - 1 Jan 2014

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-014-2721-3

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title = "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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AB - 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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Topological minors in line graphs - A proof of Zha's conjecture

Abstract

ASJC Scopus subject areas

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