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Graphs and Combinatorics

, Volume 35, Issue 2, pp 551–557 | Cite as

Rooted Complete Minors in Line Graphs with a Kempe Coloring

  • Matthias Kriesell
  • Samuel MohrEmail author
Original Paper
  • 7 Downloads

Abstract

It has been conjectured that if a finite graph has a vertex coloring such that the union of any two color classes induces a connected graph, then for every set T of vertices containing exactly one member from each color class there exists a complete minor such that T contains exactly one member from each branching set. Here we prove the statement for line graphs.

Keywords

Coloring Clique minor Kempe coloring Line graph 

Mathematics Subject Classification

05c15 05c40 

Notes

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für Mathematik der Technischen Universität IlmenauIlmenauGermany

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