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2020 Simple graphs of order 12 and minimum degree 6 contain $K_6$ minors
Ryan Odeneal, Andrei Pavelescu
Involve 13(5): 829-843 (2020). DOI: 10.2140/involve.2020.13.829

Abstract

We prove that every simple graph of order 12 which has minimum degree 6 contains a K6 minor, thus proving Jørgensen’s conjecture for graphs of order 12. In the process, we establish several lemmata linking the existence of K6 minors for graphs to their size or degree sequence, by means of their clique sum structure. We also establish an upper bound for the order of graphs where the 6-connected condition is necessary for Jørgensen’s conjecture.

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Ryan Odeneal. Andrei Pavelescu. "Simple graphs of order 12 and minimum degree 6 contain $K_6$ minors." Involve 13 (5) 829 - 843, 2020. https://doi.org/10.2140/involve.2020.13.829

Information

Received: 28 January 2020; Revised: 27 June 2020; Accepted: 28 June 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190441
Digital Object Identifier: 10.2140/involve.2020.13.829

Subjects:
Primary: 05C10, 05C83

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 5 • 2020
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