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On the Embeddability of Small Cubic ...

Kramer, Marie,

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On the Embeddability of Small Cubic Graphs Into the Torus /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On the Embeddability of Small Cubic Graphs Into the Torus // Marie Kramer.
作者:	Kramer, Marie,
面頁冊數:	1 electronic resource (159 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31932844
ISBN:	9798280784536

On the Embeddability of Small Cubic Graphs Into the Torus /
Kramer, Marie,

On the Embeddability of Small Cubic Graphs Into the Torus /Marie Kramer. - 1 electronic resource (159 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

The embeddability of graphs into different surfaces has been studied for nearly a century. In 1930, Kuratowski famously proved that a graph is planar if and only if it does not contain the complete graph K5 or the complete bipartite graph K3,3 as a topological minor. In particular, K3,3 is the only cubic obstructions for the plane. This sparked interest in two different directions: What are analogous results for other surfaces, and what can be said about embeddings of K5 and K3,3 into other surfaces? Regarding the first question, it was shown in the 1970s and 80s by Glover, Huneke, Wang, and Archdeacon that a graph is projective planar if and only if it does not contain one of 103 graphs as a topological minor. For other surfaces, such as the torus, there are partial results at best, many of which have been obtained using computer algorithms. Regarding the embeddability of K5 and K3,3 into other surfaces, Mohar classified their embeddings into the real projective plane, while Gagarin, Kocay, and Neilson classified their embeddings into the torus.The main objective of this dissertation is to obtain a theoretical proof that the set of cubic torus obstructions of Betti number at most eight consists of ten graphs, and to specify these graphs. Our second main result is a classification of toroidal embeddings of the six cubic projective plane obstructions.

English

ISBN: 9798280784536Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Topological graph theory

On the Embeddability of Small Cubic Graphs Into the Torus /
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653 $a Cubic graphs
653 $a Surfaces
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690 $a 0642
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