Geodesic
Annular and pants thrackles
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1.

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A thrackle is a drawing of a graph in which each pair of edges meets precisely once. Conway's Thrackle Conjecture asserts that a thrackle drawing of a graph on the plane cannot have more edges than vertices. We prove the Conjecture for thrackle drawings all of whose vertices lie on the boundaries of $d \le 3$ connected domains in the complement of the drawing. We also give a detailed description of thrackle drawings corresponding to the cases when $d=2$ (annular thrackles) and $d=3$ (pants thrackles). 
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     author = {Misereh, Grace and Nikolayevsky, Yuri},
     title = {Annular and pants thrackles},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     number = {1},
     year = {2018},
     doi = {10.23638/DMTCS-20-1-16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-16/}
}
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Misereh, Grace; Nikolayevsky, Yuri. Annular and pants thrackles. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi : 10.23638/DMTCS-20-1-16. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-16/

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