Date of Defense
A.T. White, Mathematics
For some years there has been interest among mathematicians in determining the different ways in which certain graphs can be imbedded in given surfaces. M.P. VanStraten in 1948, determined that it is possible to imbed the graph K3,3 (which is the graph representing the famous three houses, three utilities problem) in the torus in only two ways. She then used this fact to show that the graph representing the configuration of Desargues (containing K3,3 as a subgraph) has genus two. One major source of motivation for the work on imbedding problems has been their relation to coloring problems and shedding light on the Four Color Conjecture. The author studied two techniques for determining imbeddings. This paper presents the results.
Goodwin, William, "Imbedding Problems in Graph Theory" (1973). Honors Theses. 269.
Honors Thesis-Open Access