Degree-limited defective three colorings of planar graphs containing no 4-cycles or 5-cycles
This dissertation explores and advances results for several variants on a long-open problem in graph coloring. Steinberg's conjecture states that any planar graph containing no 4-cycles or 5-cycles is 3-colorable. The conjecture has remained open for more than forty years and brought a great deal of interest to coloring planar graphs with certain structural restrictions. In this dissertation, we present a new type of defective graph coloring that allows us to prove two main results advancing the state of Steinberg's conjecture. ^
Addie Eva Ruth Armstrong,
"Degree-limited defective three colorings of planar graphs containing no 4-cycles or 5-cycles"
Dissertations and Master's Theses (Campus Access).