SEMINAR: Groups and Combinatorics Seminar: Generalized Thrackle and Graph Surface Embeddings
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Groups and Combinatorics Seminar: Generalized Thrackle and Graph Surface Embeddings |
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Time and place: 15:00 Friday 6 November in MLR1.
Speaker: Yian Xu (University of Western Australia)
Title: Generalized Thrackle and Graph Surface Embeddings
Abstract: A thrackle on a surface X is a graph of size e and order n drawn on X such that every two distinct edges of G meet exactly once either at their common endpoint, or at a proper crossing. An unsolved conjecture of Conway (1969) asserts that e is at most n for every thrackle on a sphere. Until now, the best known bound is that e is at most 1.428n. By using discharging rules we show that e is at most 1.4n. Furthermore we show that the following are equivalent: G has a drawing on X where every two edges meet an odd number of times (a generalized thrackle); G has a drawing on X where every two edges meet exactly once (a one-thrackle); G has a special embedding on a surface whose genus differs from the genus of X by at most one.
Contact |
Gabriel Verret
<[email protected]>
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Start |
Fri, 06 Nov 2015 15:00
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End |
Fri, 06 Nov 2015 16:00
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Submitted by |
Gabriel Verret <[email protected]>
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Last Updated |
Wed, 04 Nov 2015 12:26
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