Coloring Graphs Drawn with Crossings

This dissertation will examine various results for graph colorings. It begins by introducing some basic graph theory concepts, focusing on those ideas relevant to graph embeddings, and by introducing terminology to allow a formal discussion of drawings of graphs. Chapter 2 focuses on results for pro...

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Main Author:	Guillot, Daniel Allen
Other Authors:	Oporowski, Bogdan
Format:	Others
Language:	en
Published:	LSU 2014
Subjects:	Mathematics
Online Access:	http://etd.lsu.edu/docs/available/etd-07092014-113110/

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spelling	ndltd-LSU-oai-etd.lsu.edu-etd-07092014-1131102014-07-16T03:52:10Z Coloring Graphs Drawn with Crossings Guillot, Daniel Allen Mathematics This dissertation will examine various results for graph colorings. It begins by introducing some basic graph theory concepts, focusing on those ideas relevant to graph embeddings, and by introducing terminology to allow a formal discussion of drawings of graphs. Chapter 2 focuses on results for proper colorings of graphs with good drawings, using a previous result from Král and Stacho as inspiration. Chapter 3 expands on the ideas of Chapter 2 and focuses on cyclic colorings of embedded graphs. Chapters 5 and 6 examine results for total and list colorings, respectively, of drawings of graphs. Finally, Chapter 6 introduces generalized pseudosurfaces and examines results for proper and cyclic colorings of graphs embedded in generalized pseudosurfaces. Oporowski, Bogdan Ding, Guoli Oxley, James Perlis, Robert Litherland, Richard Busch, Konstantin LSU 2014-07-15 text application/pdf http://etd.lsu.edu/docs/available/etd-07092014-113110/ http://etd.lsu.edu/docs/available/etd-07092014-113110/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.
collection	NDLTD
language	en
format	Others
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics Guillot, Daniel Allen Coloring Graphs Drawn with Crossings
description	This dissertation will examine various results for graph colorings. It begins by introducing some basic graph theory concepts, focusing on those ideas relevant to graph embeddings, and by introducing terminology to allow a formal discussion of drawings of graphs. Chapter 2 focuses on results for proper colorings of graphs with good drawings, using a previous result from Král and Stacho as inspiration. Chapter 3 expands on the ideas of Chapter 2 and focuses on cyclic colorings of embedded graphs. Chapters 5 and 6 examine results for total and list colorings, respectively, of drawings of graphs. Finally, Chapter 6 introduces generalized pseudosurfaces and examines results for proper and cyclic colorings of graphs embedded in generalized pseudosurfaces.
author2	Oporowski, Bogdan
author_facet	Oporowski, Bogdan Guillot, Daniel Allen
author	Guillot, Daniel Allen
author_sort	Guillot, Daniel Allen
title	Coloring Graphs Drawn with Crossings
title_short	Coloring Graphs Drawn with Crossings
title_full	Coloring Graphs Drawn with Crossings
title_fullStr	Coloring Graphs Drawn with Crossings
title_full_unstemmed	Coloring Graphs Drawn with Crossings
title_sort	coloring graphs drawn with crossings
publisher	LSU
publishDate	2014
url	http://etd.lsu.edu/docs/available/etd-07092014-113110/
work_keys_str_mv	AT guillotdanielallen coloringgraphsdrawnwithcrossings
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Coloring Graphs Drawn with Crossings

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