THEOREM OF THE DAY: The Euler–Hierholzer “Bridges of Konigsberg” Theorem

Theorem

A connected graph G has an Euler tour if and only if every vertex has even degree.

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Euler discovered his necessary condition (the ‘only if’ part of the theorem) in 1736 as a solution to the famous “Bridges o f Konigsberg” problem, foreshadowing thereby the study of top ¨ ology and graph theory. It was proved su fficient in 1873 by Carl Hierholzer.