PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS

A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph...

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Bibliographic Details
Main Author: Hearon, Sean M
Format: Others
Published: CSUSB ScholarWorks 2016
Subjects:
Graphs
Combinatorics
Planar
Biplanar
Graph thickness
Discrete Mathematics and Combinatorics
Online Access:https://scholarworks.lib.csusb.edu/etd/427
https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=1485&context=etd
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spelling ndltd-csusb.edu-oai-scholarworks.lib.csusb.edu-etd-14852019-10-23T03:36:29Z PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS Hearon, Sean M A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar. 2016-12-01T08:00:00Z text application/pdf https://scholarworks.lib.csusb.edu/etd/427 https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=1485&context=etd Electronic Theses, Projects, and Dissertations CSUSB ScholarWorks Graphs Combinatorics Planar Biplanar Graph thickness Discrete Mathematics and Combinatorics
collection NDLTD
format Others
sources NDLTD
topic Graphs
Combinatorics
Planar
Biplanar
Graph thickness
Discrete Mathematics and Combinatorics
spellingShingle Graphs
Combinatorics
Planar
Biplanar
Graph thickness
Discrete Mathematics and Combinatorics
Hearon, Sean M
PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
description A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.
author Hearon, Sean M
author_facet Hearon, Sean M
author_sort Hearon, Sean M
title PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
title_short PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
title_full PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
title_fullStr PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
title_full_unstemmed PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
title_sort planar graphs, biplanar graphs and graph thickness
publisher CSUSB ScholarWorks
publishDate 2016
url https://scholarworks.lib.csusb.edu/etd/427
https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=1485&context=etd
work_keys_str_mv AT hearonseanm planargraphsbiplanargraphsandgraphthickness
_version_ 1719275698333417472

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