Editing Leonhard Euler (section)

===Graph theory===
[[File:Konigsberg bridges.png|frame|right|Map of [[Königsberg]] in Euler's time showing the actual layout of the [[Seven Bridges of Königsberg|seven bridges]], highlighting the river [[Pregolya|Pregel]] and the bridges]]
In 1735, Euler presented a solution to the problem known as the [[Seven Bridges of Königsberg]].<ref name="bridge"/> The city of [[Königsberg]], [[Kingdom of Prussia|Prussia]] was set on the [[Pregolya|Pregel]] River, and included two large islands that were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once. Euler showed that it is not possible: there is no [[Eulerian path]]. This solution is considered to be the first theorem of [[graph theory]].<ref name="bridge"/>

Euler also discovered the [[Planar graph#Euler's formula|formula]] <math>V - E + F = 2</math> relating the number of vertices, edges, and faces of a [[Convex polytope|convex polyhedron]],{{sfn|Richeson|2012}} and hence of a [[planar graph]]. The constant in this formula is now known as the [[Euler characteristic]] for the graph (or other mathematical object), and is related to the [[genus (mathematics)|genus]] of the object.<ref name=gibbons/> The study and generalization of this formula, specifically by [[Augustin-Louis Cauchy|Cauchy]]<ref name="Cauchy"/> and [[Simon Antoine Jean L'Huilier|L'Huilier]],<ref name="Lhuillier"/> is at the origin of [[topology]].{{sfn|Richeson|2012}}