Browsing by Author "Hoffman, Dean"

Here we investigate the necessary and sufficient conditions for the existence of 4 - cycle systems of the line graphs of complete multipartite graphs.

Edge-colorings of graphs have a rich history and are widely studied. Trade spectra of graphs are relatively new and ripe for study. The color-trade-spectrum of a graph G is defined to be the set of all t for which there ...

In the late 1980's the intersection problem for maximum packings of K_n with triples was solved by Hoffman, Lindner, and Quattrocchi. Their combined results showed that for any n = i mod(6) such that i in { 0, 2, 4, 5} the ...

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 ...

Given a square grid of land, which has n rows and n columns. It is required to plant trees on the land so that there are k trees in every row and column and there is at most 1 tree in any small square part of the land with ...

The National Council of Teachers of Mathematics has challenged all mathematics teachers to use the Standards documents (1989, 1991, 1995, & 2000) as guidelines for teaching mathematics. Many pre-service programs are now ...

The fractional analogues of domination and packing in a graph form an interesting pair of dual linear programs, in that the feasible vectors for both LPs have interpretations as functions from the vertices of the graph to ...

We examine the problem of k-star decompositions on lambda-fold complete multipartite graphs. After a brief examination of the computational complexity issues involved, we present complete proofs for necessary and sufficient ...

In this thesis we analyze two papers, both by Dr. Stephen G. Hartke and Dr. Aparna W. Higginson, on maximum and minimum degrees of a graph $G$ under iterated line graph operations. Let $\Delta_{k}$ and $\delta_{k}$ denote ...