Seven Bridges of Königsberg
A graph "G", or one of its subgraphs, is said to be Eulerian if each of its vertices has an even number of incident edges (this number is called the degree of the vertex). This property is named after Leonhard Euler who proved in 1736, in his work on the Seven Bridges of Königsberg, that a connected graph has a tour that visits each edge exactly once if and only if it is Eulerian. However, an Eulerian subgraph does not need to be connected; for instance, the empty graph, in which all vertices are disconnected from each other, is Eulerian. The cycle space of a graph is the collection of its Eulerian spanning subgraphs.