Planar Doodles: Their Properties, Codes and Classification

Autor:	Bartholomew, Andrew, Fenn, Roger
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology 05C10 05A05 05B30 57M15 57M25
Druh dokumentu:	Working Paper
Popis:	We present those properties of planar doodles, especially when regarded as 4-valent graphs, that enable us to classify them into {\it prime} and {\it super prime} doodles by analogy to a knot sum. We describe a method for partially characterising a doodle diagram by a {\it doodle code} that describes the complementary regions of the diagram and use that code to enumerate all possible prime and super prime doodle diagrams via their dual graph. In addition we explore the relationship between planar doodles and twin groups, and note that a theorem of Tutte means that super prime doodles have a Hamiltonian circuit. We hope to expand upon this last point in a follow-up paper. Comment: 28 pages, many figures and tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2308.08834 Zobrazit plný text záznamu View this record from Arxiv