Coloring Graphs Drawn with Crossings
Guillot, Daniel Allen · 2014
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.