On the Bounds of Conway’s Thrackles
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 ≤ n for every thrackle on a sphere. Until now, the best kno...
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| Veröffentlicht in: | Discrete & computational geometry 2017-09, Vol.58 (2), p.410-416 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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
≤
n
for every thrackle on a sphere. Until now, the best known bound is
e
≤
1.428
n
. By using discharging rules we show that
e
≤
1.4
n
-
1.4
. |
|---|---|
| ISSN: | 0179-5376 1432-0444 |
| DOI: | 10.1007/s00454-017-9877-8 |