query: Proving center of a tree consists of one vertex or two adjacent vertices
positive_passages.docid: 153227
positive_passages.text: Connected graph with minimum distance
negative_passages.docid: 89452
negative_passages.text: Proof about Graph with no triangle
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: 123103
negative_passages.text: Prove recursive formula for number of spanning trees in complete graph.
negative_passages.docid: 34210
negative_passages.text: Connecting square vertexes with minimal road
negative_passages.docid: 39753
negative_passages.text: Proving that in a simple graph with $n$ vertices, two vertices have the same degree
negative_passages.docid: 13767
negative_passages.text: Number of nodes in binary tree given number of leaves
negative_passages.docid: 116538
negative_passages.text: Proof of Connected Diagrams
negative_passages.docid: 126499
negative_passages.text: Proofing a Reachable Node Algorithm for Graphs
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: 79040
negative_passages.text: Graph of $|x| + |y| = 1$
negative_passages.docid: 148376
negative_passages.text: Proving that a Binary Tree of $n$ nodes has a height of at least $\log(n)$.
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: 79631
negative_passages.text: Find a graph on eight vertices with a pair of pseudosimilar vertices
negative_passages.docid: 89493
negative_passages.text: Prove that circumcentre of $ABH,BCH,CAH$ are the vertices of a triangle congruent to $ABC$
negative_passages.docid: 2794
negative_passages.text: Prove that if a group contains exactly one element of order 2, then that element is in the center of the group.
negative_passages.docid: 11393
negative_passages.text: The center of the dihedral group