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  "body": "\n## Example\n\nThe city of Königsberg had four land areas, joined by seven bridges over the river Pregel.\nThe problem asked for a walk that crosses each bridge exactly once.\n\nModel each land area as a vertex and each bridge as an edge. This gives a connected [[multigraph|01M5T0KDG7]] with $4$ vertices and $7$ edges.\nThe degrees of the vertices are $5$, $3$, $3$ and $3$.\nAn [[Eulerian trail|0NNYDD1AVR]] can have at most two vertices of odd degree, by the theorem on [[degrees along an Eulerian trail|0CDVDGWGEG]].\nHere all four degrees are odd, so the walk does not exist.\n\n## Remarks\n\nLeonhard Euler solved the problem in 1736. His analysis is often seen as the start of graph theory.\nThe problem has no solution even if the walk does not have to return to its start.\n\n## Explanations\n\n### L1 human\n\nEach time a walk passes through a land area, it uses two bridges there, one to enter and one to leave.\nSo a land area in the middle of the walk needs an even number of bridges.\nKönigsberg had four land areas with an odd number of bridges.\n",
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