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- W2989896095 abstract "A drawing of a graph in the plane is a thrackle if every pair of edges intersects exactly once, either at a common vertex or at a proper crossing. Conway’s conjecture states that a thrackle has at most as many edges as vertices. In this paper, we investigate the edge-vertex ratio of maximal thrackles, that is, thrackles in which no edge between already existing vertices can be inserted such that the resulting drawing remains a thrackle. For maximal geometric and topological thrackles, we show that the edge-vertex ratio can be arbitrarily small. When forbidding isolated vertices, the edge-vertex ratio of maximal geometric thrackles can be arbitrarily close to the natural lower bound of (nicefrac {1}{2}). For maximal topological thrackles without isolated vertices, we present an infinite family with an edge-vertex ratio of (nicefrac {5}{6})." @default.
- W2989896095 created "2019-12-05" @default.
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- W2989896095 date "2019-01-01" @default.
- W2989896095 modified "2023-10-03" @default.
- W2989896095 title "On the Edge-Vertex Ratio of Maximal Thrackles" @default.
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- W2989896095 doi "https://doi.org/10.1007/978-3-030-35802-0_37" @default.
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