query: If G is connected and order = size - 1 G is a Tree
positive_passages.docid: 146016
positive_passages.text: no cycles if and only if has $n-m$ connected components
negative_passages.docid: 65574
negative_passages.text: How to prove that total number of non-isomorphic labelled trees of order $n$ is $n^{n-2}$?
negative_passages.docid: 122998
negative_passages.text: number of edges induction proof
negative_passages.docid: 85852
negative_passages.text: How many total order relations on a set $A$?
negative_passages.docid: 117992
negative_passages.text: Help with graph induction proof
negative_passages.docid: 87760
negative_passages.text: Determine the diameter of a graph of order $n \geq 3$ where $\delta (G) \geq \frac{n-1}{2}$.
negative_passages.docid: 131031
negative_passages.text: Q: Proving G is d-colorable
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: 108631
negative_passages.text: Calulating the Ramsey number $R(T, K_{1,n})$ of a tree $T$ and bipartite graph $K_{1,n}$
negative_passages.docid: 62455
negative_passages.text: Prove Equivalence Relation in G
negative_passages.docid: 1453
negative_passages.text: Prove that the graph is connected
negative_passages.docid: 33300
negative_passages.text: Showing order of $Z (G) =1$ or $pq$
negative_passages.docid: 23008
negative_passages.text: For all $1 \leq i < j \leq k$, the subtrees $T_i$ and $T_j$ have a vertex in common. Show that $T$ has a vertex which is in all of the $T_i$.
negative_passages.docid: 127277
negative_passages.text: Graph Theory: Tree has at least 2 vertices of degree 1
negative_passages.docid: 79055
negative_passages.text: Orders of a symmetric group
negative_passages.docid: 39100
negative_passages.text: Exercise from Serre's "Trees" - prove that a given group is trivial
negative_passages.docid: 82578
negative_passages.text: Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$