query: Prove or disprove: for all graphs $G = (V, E)$, if $|E| = |V| - 1$ then $G$ is a tree.
positive_passages.docid: 158083
positive_passages.text: If $G$ is a connected graph with $n$ vertices and $n - 1$ edges then $G$ is a tree, using Induction.
negative_passages.docid: 122828
negative_passages.text: Proof that TREE(n) where n >= 3 is finite?
negative_passages.docid: 27373
negative_passages.text: Graph Proof by induction.
negative_passages.docid: 44729
negative_passages.text: Prove $g$ is a generator if $g^q=1 \pmod p$
negative_passages.docid: 91253
negative_passages.text: Proving that every graph that each vertex at degree 2 must contain a cycle
negative_passages.docid: 147282
negative_passages.text: Prove that in every graph with at least two vertices, there are at least two vertices which have the same degree?
negative_passages.docid: 151521
negative_passages.text: Set Theory: Tree Property
negative_passages.docid: 42367
negative_passages.text: Prove that simple graph $G$ is orientable
negative_passages.docid: 17077
negative_passages.text: Prove or disprove: If $H$ and $G/H$ are cyclic, then $G$ is cyclic.
negative_passages.docid: 48692
negative_passages.text: A problem about the graph theory
negative_passages.docid: 144732
negative_passages.text: If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
negative_passages.docid: 49045
negative_passages.text: Graph theory: Tree holds two sub-tree with an amount of vertices
negative_passages.docid: 122998
negative_passages.text: number of edges induction proof
negative_passages.docid: 49703
negative_passages.text: Analogue of closed graph theorem
negative_passages.docid: 120617
negative_passages.text: No cycle containing edges $e$ and $g$ implies there is a vertex $u$ so that every path sharing one end with $e$ and another with $g$ contains $u$
negative_passages.docid: 127818
negative_passages.text: How do I prove that a graph is a topological manifold
negative_passages.docid: 127965
negative_passages.text: Graph theory (Graph Connectivity)