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Browsing by Author "Lindner, Charles"

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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 ...

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 ...

The Intersection Problem for Maximum Packings of the Complete Graph with 4-Cycles 

Cortez, Joseph (2020-05-11)
A maximum packing of K_n with 4-cycles may leave some edges of the graph unpacked. The size of the leave is determined by the congruence class of n modulo 8. When n ≡ 1 (mod 8) the packing coincides with a 4-cycle system ...

The Metamorphosis of 2-fold Triple Systems into Maximum Packings of 2Kn with 4-cycles 

McClanahan, Stacie (2011-04-27)
The graph is called a hinge. A hinge system of order n is a pair (X, H) where H is a collection of edge disjoint hinges which partition the edge set of 2Kn with vertex set X. Let (X, H) be a hinge system and D the collection ...

A New Solution to the Intersection Problem of Mendelsohn Triple Systems 

Watson, Rachel (2012-03-29)
The thesis provides an alternate solution to the intersection problem, in which the goal is to determine the set of all values for which there exists a pair of Mendelsohn Triple Systems having this exact value of cyclic ...

Revisiting the Intersection Problem for Maximum Packings of K_(6n+5) with Triples 

Holmes, Amber (2017-04-16)
In 1989, Gaetano Quattrocchi gave a complete solution of the intersection problem for maximum packings of K_(6n+5) with triples when the leave (a 4--cycle) is the same in each maximum packing. Quattrocchi showed that I[2]=2 ...