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Physical Sciences and Mathematics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Tournaments And A Fibonacci Link, Michael Long, Daniela Genova
Tournaments And A Fibonacci Link, Michael Long, Daniela Genova
Showcase of Osprey Advancements in Research and Scholarship (SOARS)
Round robin tournaments are a type of directed graphs with applications to athletic competitions and transportation logistics. The presentation begins with a brief series of informative theorems and properties of directed graphs, which are imperative to our understanding of the properties that make directed graphs (and, subsequently, round robin tournaments) uniquely interesting. We then present a number of results about the properties of tournaments (defined as a complete directed graph), including transitivity–a relatively uncommon property used to determine domination in a round robin tournament–and connectivity, which can most often be seen in determining means of transportation between any two locations. …
Block Designs, Lucien Poulin, Daniela Genova
Block Designs, Lucien Poulin, Daniela Genova
Showcase of Osprey Advancements in Research and Scholarship (SOARS)
Block designs are a type of combinatorial structures that can be used to model many different types of problems ranging from experimental design to computer software testing. They can be used to construct schemes that ensure complete optimization and efficiency of the given experiment. We focus mainly on Steiner and Kirkman triple systems, as well as, on different ways for constructing block designs. Well known results in combinatorics such as Fisher’s inequality and Kirkman’s schoolgirl problem are also discussed.
Embedding Graphs On Surfaces And Graph Minors, Tracy Leung, Mya Salas, Dylan Wilson
Embedding Graphs On Surfaces And Graph Minors, Tracy Leung, Mya Salas, Dylan Wilson
Showcase of Osprey Advancements in Research and Scholarship (SOARS)
A planar graph is a graph that can be drawn in such a way in the plane, so that no edges cross each other. In other words, it is a graph that can be embedded in the plane. We discuss the conditions that make a graph embeddable on a sphere with k handles. Then, using vertex deletions and edge contractions, which produce graph minors, we examine if a graph is minimally nonembeddable on a surface. To conclude, we discuss an important result, that the set of minimally nonembeddable graphs on a surface is finite.