query: Prove that a connected graph with $n$ vertices is a tree iff it has $n-1$ edges.
positive_passages.docid: 145718
positive_passages.text: Proving that A connected graph on $n$ vertices is a tree iff it has $n-1$ edges
negative_passages.docid: 124848
negative_passages.text: Why $O(n)$ has exactly two connected components?
negative_passages.docid: 84654
negative_passages.text: The graph of xy = 1 is connected or not
negative_passages.docid: 96620
negative_passages.text: Condition on degrees for existence of a tree
negative_passages.docid: 117685
negative_passages.text: Prove that a bipartite planar graph has a vertex of degree at most 3
negative_passages.docid: 101520
negative_passages.text: Let $G$ be a graph of minimum degree $k>1$. Show that $G$ has a cycle of length at least $k+1$
negative_passages.docid: 1453
negative_passages.text: Prove that the graph is connected
negative_passages.docid: 33316
negative_passages.text: Show that if $G$ is simple a graph with $n$ vertices and 􏰈the number of edges $m>\binom{n-1}{2}$, then $G$ is connected.
negative_passages.docid: 39100
negative_passages.text: Exercise from Serre's "Trees" - prove that a given group is trivial
negative_passages.docid: 9847
negative_passages.text: Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord.
negative_passages.docid: 158802
negative_passages.text: Graph theory and tree company
negative_passages.docid: 99931
negative_passages.text: Number of connected graphs on labeled vertices, counted according to parity
negative_passages.docid: 83872
negative_passages.text: Isomorphisms for graphs with loops and multiple edges
negative_passages.docid: 126428
negative_passages.text: Prove the edges of a multigraph may be oriented such that the net-degree of any vertex is $\leq 1$.
negative_passages.docid: 10910
negative_passages.text: How many edges does an undirected tree with $n$ nodes have?
negative_passages.docid: 131736
negative_passages.text: Proving a triangle with different edge colors exists in a graph.
negative_passages.docid: 86271
negative_passages.text: Spanning Trees: Prove if $e_1$ is an edge in $X$ that isn't in $Y$, then there exists an edge ...