Thrackles containing a standard musquash

Research paper by Grace Misereh, Yuri Nikolayevsky

Indexed on: 21 Jan '16Published on: 21 Jan '16Published in: Mathematics - Combinatorics


A thrackle is a drawing of a graph in which each pair of edges meets precisely once. Conway's Thrackle Conjecture asserts that a planar thrackle drawing of a graph cannot have more edges than vertices, which is equivalent to saying that no connected component of the graph contains more than one cycle. We prove that a thrackle drawing containing a standard musquash (standard $n$-gonal thrackle) cannot contain any other cycle of length three or five.