大圆圈树刺
Great-circle Tree Thrackles
摘要：
一个thrackle是一个图形绘图，其中每对边缘满足一次。Thrackle猜想（由John Conway建立）指出，Thrackle的边数不能超过它的顶点数。Cairns，Koussas，and Nikolayevsky（2015）证明了Thrackle猜想对于在球面上画的大圆Thrackle成立。他们还指出，Thrackle猜想可以重述说，一个图可以画成一个thrackle图在平面上，当且仅当它允许一个大圆thrackle图。我们证明了这类大圆可攻图不包括某些树。因此，凯恩斯、库萨斯和尼古拉耶夫斯基（2015）的非正式猜想并不等价于萨拉克猜想。
英文摘要：
A thrackle is a graph drawing in which every pair of edges meets exactly once. The Thrackle Conjecture (established by John Conway) states that the number of edges of a thrackle cannot exceed the number of its vertices. Cairns, Koussas, and Nikolayevsky (2015) prove that the Thrackle Conjecture holds for great-circle thrackles drawn on the sphere. They also posit that the Thrackle Conjecture can be restated to say that a graph can be drawn as a thrackle drawing in the plane if and only if it admits a great-circle thrackle drawing. We demonstrate that the class of great-circle thrackleable graphs excludes some trees. Thus the informal conjecture from Cairns, Koussas, and Nikolayevsky (2015) is not equivalent to the Thrackle Conjecture.
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