Sciweavers

Share
COMGEO
2011
ACM

A computational approach to Conway's thrackle conjecture

8 years 1 months ago
A computational approach to Conway's thrackle conjecture
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 50 years old conjecture of Conway, t(n) = n for every n ≥ 3. For any ε > 0, we give an algorithm terminating in eO((1/ε2 ) ln(1/ε)) steps to decide whether t(n) ≤ (1 + ε)n for all n ≥ 3. Using this approach, we improve the best known upper bound, t(n) ≤ 3 2 (n − 1), due to Cairns and Nikolayevsky, to 167
Radoslav Fulek, János Pach
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where COMGEO
Authors Radoslav Fulek, János Pach
Comments (0)
books