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Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon
Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon
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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.