In the article we offer the historical background of the well-known and still actual problem, the Minimum Spanning Tree Problem, first. We switch from the original formulation given by the Czech mathematician Otakar Bor􀄤vka to an up-to-date formulation based on the graph theory terminology and introduce basic methods solving this problem.
This is followed by the illustration of how the Minimum Spanning Tree Problem can influence our approach to the explanation of some other famous graph problems taught in the frame of the subject Graph Theory. Especially, on the base of the Jarník’s solution of the Minimum Spanning Tree Problem, we describe Dijkstra’s method for finding the shortest path and both important searching methods, Depth-First-Search and Breadth-First-Search.