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The Hanani-Tutte Theorem and Non-separating Planar Graphs

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thesis
posted on 04.04.2020 by Hooman Reisi Dehkordi
Graphs are a useful data structure for representing networks of relationships among objects. Drawings of graphs help humans to comprehend graphs better. We study several types of drawings such as planar drawings, in which edges do not cross, and superthrackles, in which any two edges cross. We show how to reduce the number of crossings in certain drawings to obtain a planar drawing or a superthrackle drawing. Moreover, we introduce a class of planar graphs that cannot be disconnected by removal of a cycle, determine its fundamental properties and use it to prove results about crossings in drawings of graphs.

History

Campus location

Australia

Principal supervisor

Graham Ernest Farr

Additional supervisor 1

David Wood

Additional supervisor 2

Peter Eades

Year of Award

2020

Department, School or Centre

Clayton School of IT

Course

Doctor of Philosophy

Degree Type

DOCTORATE

Exports