Semester of Graduation

Summer 2026

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

Abstract

In a connected graph with weights on the edges, a minimum-weight spanning tree can be obtained by repeatedly choosing minimum-weight edges while avoiding choosing the edge set of any cycle. This algorithm is known as Kruskal’s Algorithm, although it was first introduced by Boruvka in 1926. Prim introduced an alternative algorithm in which, at each step, the chosen set of edges forms a connected graph. Both of these algorithms make locally optimal choices that eventually yield a global optimum. This thesis considers how these algorithms can be extended to matroids. In particular, it is shown that matroids are exactly the structures for which a certain greedy algorithm always produces an optimal set. It is also shown how Dawson extended Prim’s Algorithm to matroids in 1982.

Date

5-8-2026

Committee Chair

James Oxley

LSU Acknowledgement

1

LSU Accessibility Acknowledgment

1

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