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

A simple graph, G, avoids a k-rainbow edge coloring if any color appears on at least k + 1 edges of G. For any positive integer k, the k-Anti-Ramsey Number, ARk(G,H), is the maximum number of colors in an edge coloring of ...

The choice numbers of some complete k−partite graphs are found, after we resolved a dispute regarding the choice number of K(4, 2, . . . , 2) when k is odd. Estimates of the choice numbers and the Ohba numbers of K(m, ...

In this thesis, the decomposition problem of graphs with two associate classes into paths of length 3 is completely settled. The intersection problem for latin rectangles is completely solved as well. In addition, an ...

A graph G is edge-regular with parameters n, d, and λ if V(G)=n, the degree of every vertex of G is d, and for any pair of adjacent vertices u and v, N_G(u)∩N_G(v)=λ. We say such graphs are in ER(n,d,λ). In this dissertation ...

A $C_4$-decomposition of $K_v - F$, where $F$ is a $1$-factor of $K_v$ and $C_4$ is the cycle on $4$ vertices, is a partition $P$ of $E(K_v - F)$ into sets, each element of which induces a $C_4$ (called a block). A function ...

We are given an n x n array, ML(n,k), with integers n, d, k > 0 such that n=mk and each symbol in {0, ..., m-1} appears in each row and column of the ML(n,k) exactly k times. We aim to construct an ML_d(n,k) with the ...

All graphs in this paper are both finite and simple. α(G) is the vertex independence of a graph, G. The Hall ratio of G is defined as ρ(G) = max[n(H) /α(H) |n(H) = |V (H)|and H ⊆ G] where H ⊆ G means that H is a subgraph of ...

A graph G is a pair (V, E) where V is the set of vertices(or nodes) and E is the set of edges connecting the vertices. A graph is called k-regular, if all of its vertices are incident with k edges. A k-factor of a graph G ...

The conjecture that $\alpha(G) \geq \gamma'(G)$ is unproven where $\alpha(G)$ is the vertex independence number and $\gamma'(G)$ is the inverse domination number of a simple graph G. We have found the conjecture to be true ...

For integers 1 =< m < n and a prime p (we require 2 =< m when p = 2), a subset I(p^n; p^m) ={0,...,p^n-1} is described which contains no pm-term cyclic arithmetic progression modulo p^n, and which is maximal among subsets ...