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Seven bridges of konigsberg

Seven Bridges of Konigsberg

Seven Bridges of Konigsberg was first resolved by Leonard Euler in 18th century. The city of Konigsberg was set on both sides of the pregal river. The two large island and the mainland is connected by seven bridges. The problem was that a person walks through the city must cross each bridge only once. Every bridge must be crossed completely and one could not walk half way or use any route other than the bridges. The walk should start and end at the same point.

Euler proved that there is no solution for this problem. He formulated this problem by leaving all other features. He took only the list of land masses and the bridges connecting them. He replaced the land masses with the Vertex or node. He represented the bridges and the land masses graphically. This problem laid foundation for the graph theory and prefigured the idea of Topology.

In graphical theory, Euler proved that if a network has more than two odd vertices, it does not have an Euler path. To have Euler path, the number of bridges touching the land masses must be even. But in original problem all four land masses are touched by the odd number of bridges.

Euler theory shows that the desired network must have exactly zero or two nodes of odd degree. The result stated by Euler was proved to be sufficient. So to honor him, it was called Euler path.

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