How Many Edges Does A Minimum Spanning Tree For G Have? As a minimum spanning tree is also a spanning tree, these properties will also be true for a minimum spanning tree. vertices, and each of the spanning trees contains four edges. A spanning tree doesn’t contain any loops or cycles. contain any loops or
Can Undirected Graphs Have Cycles? An undirected graph is acyclic (i.e., a forest) if a DFS yields no back edges. Since back edges are those edges ( u , v ) connecting a vertex u to an ancestor v in a depth-first tree, so no back edges means there are only tree edges, so there
Can A Minimum Spanning Tree Contain A Cycle? A spanning tree can never contain a cycle. Spanning tree is always minimally connected i.e. if we remove one edge from the spanning tree, it will become disconnected. A spanning tree is maximally acyclic i.e. if we add one edge to the spanning tree, it will create