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Simple graphs
of order 12 and minimum degree 6 contain $K_6$ minors
Ryan Odeneal and Andrei Pavelescu
Vol. 13 (2020), No. 5, 829–843
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Abstract |
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We prove that every simple graph of order 12 which has minimum degree 6 contains a minor, thus proving Jørgensen’s conjecture for graphs of order 12. In the process, we establish several lemmata linking the existence of 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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Keywords
Jorgensen's conjecture, $K_6$ minors, minimum degree 6
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Mathematical Subject Classification 2010
Primary: 05C10, 05C83
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Milestones
Received: 28 January 2020
Revised: 27 June 2020
Accepted: 28 June 2020
Published: 5 December 2020
Communicated by Ronald Gould
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Authors |
| Ryan Odeneal | |
| Department of Mathematics and
Statistics University of South Alabama Mobile, AL United States |
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| Andrei Pavelescu | |
| Department of Mathematics and
Statistics University of South Alabama Mobile, AL United States |
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