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- W4386044511 abstract "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." @default.
- W4386044511 created "2023-08-22" @default.
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- W4386044511 date "2023-08-17" @default.
- W4386044511 modified "2023-09-25" @default.
- W4386044511 title "Planar Doodles: Their Properties, Codes and Classification" @default.
- W4386044511 doi "https://doi.org/10.48550/arxiv.2308.08834" @default.
- W4386044511 hasPublicationYear "2023" @default.
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