Discrete Mathematics and Combinatorics Commons^™

Polychromatic Colorings Of Certain Subgraphs Of Complete Graphs And Maximum Densities Of Substructures Of A Hypercube, Ryan Tyler Hansen

Graduate Theses, Dissertations, and Problem Reports

If G is a graph and H is a set of subgraphs of G, an edge-coloring of G is H-polychromatic if every graph from H gets all colors present in G on its edges. The H-polychromatic number of G, poly_HG, is the largest number of colors in an H-polychromatic coloring. We determine poly_HG exactly when G is a complete graph on n vertices, q a fixed nonnegative integer, and H is the family of one of: all matchings spanning n-q vertices, all 2-regular graphs spanning at least n-q vertices, or all cycles of length precisely n-q. …