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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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 |
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Graphs Combinatorics Planar Biplanar Graph thickness Discrete Mathematics and Combinatorics |
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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 |
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1719275698333417472 |