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osu1209141894.pdf (23.13 MB)
ETD Abstract Container
Abstract Header
The Kuratowski covering conjecture for graphs of order less than 10
Author Info
Hur, Suhkjin
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1209141894
Abstract Details
Year and Degree
2008, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
Kuratowski proved that a finite graph embeds in the plane if it does not contain a subdivision of either K
5
or K
3,3
, 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.
Committee
Henry H. Glover, PhD (Committee Chair)
Ian Leary, PhD (Committee Co-Chair)
Sergei Chmutov, PhD (Committee Member)
Neil Robertson, PhD (Committee Member)
Pages
383 p.
Subject Headings
Mathematics
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Citations
Hur, S. (2008).
The Kuratowski covering conjecture for graphs of order less than 10
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1209141894
APA Style (7th edition)
Hur, Suhkjin.
The Kuratowski covering conjecture for graphs of order less than 10.
2008. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1209141894.
MLA Style (8th edition)
Hur, Suhkjin. "The Kuratowski covering conjecture for graphs of order less than 10." Doctoral dissertation, Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1209141894
Chicago Manual of Style (17th edition)
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Document number:
osu1209141894
Download Count:
456
Copyright Info
© 2008, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.