Minimum spanning trees

Pallavi Jayawant; Kerry Glavin

doi:10.2140/involve.2009.2.439

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Home > Journals > Involve > Volume 2 > Issue 4 > Article

2009 Minimum spanning trees

Pallavi Jayawant, Kerry Glavin

Involve 2(4): 439-450 (2009). DOI: 10.2140/involve.2009.2.439

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Abstract

The minimum spanning tree problem originated in the 1920s when O. Borůvka identified and solved the problem during the electrification of Moravia. This graph theory problem and its numerous applications have inspired many others to look for alternate ways of finding a spanning tree of minimum weight in a weighted, connected graph since Borůvka’s time. This note presents a variant of Borůvka’s algorithm that developed during the graph theory course work of undergraduate students. We discuss the proof of the algorithm, compare it to existing algorithms, and present an implementation of the procedure in Maple.