If a graph had four vertices of odd valence, then we can duplicate two edges to eulerize the graph.

Question

Quizplus · Accepted Answer

Eulerizing a graph (making it Eulerian by adding edges) requires that all vertices have even degree. Duplicating two edges may not necessarily make all vertices of odd valence have even valence, especially if the duplicated edges are not chosen correctly or if the graph structure requires more than two edges to be added for all vertices to have even valence.

If a Graph Had Four Vertices of Odd Valence, Then