Browsing Auburn Theses and Dissertations by Author "Johnson, Peter"

Now showing items 21-29 of 29

On the Spectrum of Minimal Covers By Triples

Castellana, Vincent (2006-08-15)

A Minimal Cover by Triples is an ordered pair (V,T) where V is a finite set and T is a collection of three element subsets of V with two properties. First, that every pair of elements of V appear together in at least ...

On Translative Packing Densities in $E^2$ and $E^3$

He, Yangyang (2023-12-01) ETD File Embargoed

The theory of packing and covering is an essential part of discrete geometry. In this dissertation we focus on and contribute to the knowledge on the densities of translative and lattice packings in $E^{2}$ and ...

Path Decompositions of the Kneser Graph

Whitt, Thomas Richard, III (2013-04-22)

Necessary and sufficient conditions are given for the existence of a graph decomposition of the Kneser Graph $KG_{n,2}$ into paths of length three and four, and of the Generalized Kneser Graph $GKG_{n,3,1}$ into paths of ...

Rainbow Cycle Forbidding Edge Colorings

Owens, Andrew (2019-07-18)

It is well known that K_n can be edge colored using n-1 colors in order to avoid rainbow cycles; moreover, this is the maximum number of colors possible. We call such an edge coloring a JL-coloring. In previous work it has ...

Response-Consequence Contingency Discriminability When Positive and Negative Reinforcement Compete in Concurrent Schedules

Magoon, Michael (2005-08-15)

Four experiments were conducted to test the qualitative prediction of contingency discriminability theory that any difference in type between the consequences of concurrently available discriminated operants will heighten ...

Security, (F,I)-security, and Ultra-security in Graphs

Petrie, Caleb (2012-08-02)

Let G=(V,E) be a graph and S a subset of V. The notion of security in graphs was first presented by Brigham et al [3]. A set S is secure if every attack on S is defendable. The cardinality of a smallest secure set of G ...

The Shields-Harary Number of Graphs

Holliday, John (2004-05-15)

The Shields-Harary numbers are a class of graph paramaters that measure the robustness of a graph in terms of network vulnerability, with reference to a given cost function.

The Slow-Coloring Game on Path Power Graphs

Graves, Josey (2022-11-16)

The Slow-Coloring Game is a game played on a graph G by two players which we will refer to as Lister and Painter. In the ith round, Lister marks a nonempty subset M of V (G) of uncolored vertices as eligible to receive ...

Some Necessary Conditions for List Colorability of Graphs and a Conjecture on Completing Partial Latin Squares

Bobga, Benkam (2008-12-15)

Let C be an infinite set of symbols, F the collection of finite subsets of C. A function L is a list assignment to a graph G if L assigns to each vertex of G a finite subset of C. A proper L-coloring occurs when adjacent ...