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Browsing by Author "Hoffman, Dean"
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4-cycles systems of line graphs of complete multipartite graphs
Sehgal, Nidhi (2008-08-15)
Here we investigate the necessary and sufficient conditions for the existence of 4 - cycle systems of the line graphs of complete multipartite graphs.
Almost Resolvable Maximum Packings of Complete Bipartite Graphs with 4-Cycles
Ohlson, Vicky (2012-07-17)
A packing of a complete bipartite graph K(m,n) with 4-cycles is a decomposition of K(m,n) into a collection C of edge-disjoint 4-cycles and a set of unused edges L referred to as the leave. If C is as large as possible ...
Color Trades on Graphs
Carr, John (2022-08-03)
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 ...
Competition Graphs
Swan, Brandon (2012-04-18)
Competition graphs were originally created in 1968 by Biologist Joel Cohen. In this paper we discuss four things. First, the use of linear algebra is considered with connection to competition graphs. Second, we generalize ...
The Complete Solution of the Intersection Problem for Maximum Packings of K_n with Triples
Holmes, Amber (2018-07-03)
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 ...
Cycle Systems
Sehgal, Nidhi (2012-01-18)
In this dissertation the author has found the necessary and sufficient conditions for obtaining a 6-cycle system of the Cartesian product of two complete graphs covering 2-paths in the corresponding bipartite graph. She ...
Decomposing Graphs With Two Associate Classes Into Paths Of Length 3 And The Intersection Problem Of Latin Rectangles
Yeh, Bin (2018-07-24)
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 ...
Disjoint G-Designs and the Intersection Problem for Some Seven Edge Graphs
Hollis, Daniel (2017-04-21)
A $G$-Design of order $n$ is a decomposition of the edges of $K_n$ (the complete graph on $n$ vertices) into subgraphs of $K_n$ isomorphic to $G$, called blocks, in which each edge of $K_n$ appears in exactly one block. ...
Edge-Regular Graphs with Lambda=2
Glorioso, Vincent (2019-07-23)
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 ...
Equitable Block-Colorings of Graph-Decompositions and Tiling Generalized Petersen Graphs
Matson, Elizabeth (2018-04-23)
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 ...
Existence of TP(d,k,n)
Aliyev, Natig (2019-04-24)
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 ...
An Exploratory Study of the Impact of a Manipulatives-Intensive Fractions Unit during a Middle Grades Methods Course on Prospective Teachers’ Relational Understanding of Fractions
Peppers, Denise (2016-12-10)
“A critical pillar of a strong PreK–12 education is a well-qualified teacher in every classroom” (Conference Board of Mathematical Sciences, 2012, p. 1). In order for teachers to help students build procedural fluency from ...
Exploring Beliefs and Practices of Teachers of Secondary Mathematics Who Participated in a Standards-Based Pre-Service Education Program
Smeal, Mary (2008-12-15)
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 Chromatic Number and the Hall Ratio
Barnett, Johnathan (2016-07-29)
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 ...
Fractional Domination, Fractional Packings, and Fractional Isomorphisms of Graphs
Rubalcaba, Robert (2005-05-15)
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 ...
The Intersection Problem for Steiner Triple Systems
Fain, Bradley (2016-04-22)
A Steiner triple system of order n is a pair (S,T) where T is an edge disjoint partition
of the edge set of K_n (the complete undirected graph on n vertices with vertex set S) into triangles (or triples). It is by now ...
k-star Decompositions of Lambda-Fold Complete Multipartite Graphs
Anzur, Matthew (2007-08-15)
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 ...
K4-e Designs with a Hole
Back, Roxanne (2010-07-27)
In this paper we look at K4 − e designs on Kw−v + v. We settle the case when w and v
are of the same parity.
Maximum and minimum degree in iterated line graphs
Aggarwal, Manu (2013-06-13)
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 ...
Modular Balanced Graphs
Brown, Wesley (2012-07-02)
Necessary and sufficient conditions for the existence of modular balanced graphs and modular balanced bipartite graphs.