Question: Show that if every circuit not passing through any vertex other than its initial vertex more than once in a connected graph contains an odd number of edges, then this graph must be a cactus.
A degree-constrained spanning tree of a simple graph G is a spanning tree with the property that the degree of a vertex in this tree cannot exceed some specified bound. Degreeconstrained spanning trees are useful in models of transportation systems where the number of roads at an intersection is limited, models of communications networks where the number of links entering a node is limited, and so on.