LE3 .A278 2021

2021

Hooper, Jeff
Clarke, Nancy

Acadia University

Bachelor of Science

Honours

Mathematics and Statistics

Mathematics & Statistics

One simple way to assign labels or colours to the vertices of a graph is by using a process known as the greedy colouring algorithm. The maximum number of colours this process uses over all possible orderings of the vertices is known as the Grundy number of that graph. This process has been well studied for undirected graphs, but less attention has been paid to the Grundy number of oriented graphs which was introduced in [2]. We contribute to the theory of Grundy oriented colouring, and provide results on the Grundy oriented numbers (under the two nontrivial definitions given in [2]). In particular, new bounds for various graph classes are given, including paths, cycles, stars, windmills, and wheels.

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https://scholar.acadiau.ca/islandora/object/theses:3561