Eulerian Trail Proof. A connected graph G contains an Eulerian trail if and only if exactly 2 vertices of G have odd degree. Then G is Eulerian and the result holds.
Proof Euler Trail Theorem 1 from jeongtaebang.tistory.com
Let G VG EG be a semi-Eulerian graph. Then clearly the final vertexvp must have degree 0 in. Suppose that P is an Eulerian trail of G.
A graph is said to be Eulerian if it contains an Eulerian circuit.
Proof of 1 2. Similarly by the same result if G is Eulerian it is by definition traversable. It G has an Eulerian uv-trailif and only if a degree of every vertex in VGf uvgis evendegrees of u and v are odd and b G has at most onenontrivial component. 3 The edges of G can be partitioned into edge-disjoint cycles.
