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Full-Text Articles in Discrete Mathematics and Combinatorics
Polychromatic Colorings Of Certain Subgraphs Of Complete Graphs And Maximum Densities Of Substructures Of A Hypercube, Ryan Tyler Hansen
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, polyHG, is the largest number of colors in an H-polychromatic coloring. We determine polyHG 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. …
On Generalizations Of Supereulerian Graphs, Sulin Song
On Generalizations Of Supereulerian Graphs, Sulin Song
Graduate Theses, Dissertations, and Problem Reports
A graph is supereulerian if it has a spanning closed trail. Pulleyblank in 1979 showed that determining whether a graph is supereulerian, even when restricted to planar graphs, is NP-complete. Let $\kappa'(G)$ and $\delta(G)$ be the edge-connectivity and the minimum degree of a graph $G$, respectively. For integers $s \ge 0$ and $t \ge 0$, a graph $G$ is $(s,t)$-supereulerian if for any disjoint edge sets $X, Y \subseteq E(G)$ with $|X|\le s$ and $|Y|\le t$, $G$ has a spanning closed trail that contains $X$ and avoids $Y$. This dissertation is devoted to providing some results on $(s,t)$-supereulerian graphs and …