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The Kuratowski covering conjecture for graphs of order less than 10
Hur, Suhkjin

2008, Doctor of Philosophy, Ohio State University, Mathematics.
Kuratowski proved that a finite graph embeds in the plane if it does not contain a subdivision of either K5 or K3,3, called Kuratowski subgraphs.
A conjectured generalization of this result to all nonorientable surfaces says that a finite graph embeds in the nonorientable surface of genus g̃
if it does not contain g̃+1 Kuratowski subgraphs such that
the union of each pair of these fails to embed in the projective plane,
the union of each triple of these fails to embed in the Klein bottle if g̃ ≥ 2,
and the union of each triple of these fails to embed in the torus if g̃ ≥ 3.
We prove this conjecture for all graphs of order < 10.
Henry H. Glover, PhD (Committee Chair)
Ian Leary, PhD (Committee Co-Chair)
Sergei Chmutov, PhD (Committee Member)
Neil Robertson, PhD (Committee Member)
383 p.

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Hur, S. (2008). The Kuratowski covering conjecture for graphs of order less than 10. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Hur, Suhkjin. "The Kuratowski covering conjecture for graphs of order less than 10." Electronic Thesis or Dissertation. Ohio State University, 2008. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Hur, Suhkjin "The Kuratowski covering conjecture for graphs of order less than 10." Electronic Thesis or Dissertation. Ohio State University, 2008. https://etd.ohiolink.edu/

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