Can one cross all seven bridges of old Königsberg only once and return to start {Königsberg bridges problem}? Königsberg had seven bridges and two river islands.
Euler replaced bridges by lines and land by points to show that one path cannot traverse the bridges. Königsberg bridges problem is a topological graph, in which land is nodes and bridges are connections. If all nodes are even, one can cross all bridges once and return to start. If one or two nodes are odd, one can cross all bridges once but end at another point. If more than two nodes are odd, one must cross at least one bridge more than once.
Mathematical Sciences>Topology>Problems
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Date Modified: 2022.0224