query: Prove that any graph G with an even number of vertices has two vertices with an even number of common neighbour
positive_passages.docid: 150508
positive_passages.text: ∗∗Prove that each graph with an even number of vertices has two vertices with an even number of common neighbors.
negative_passages.docid: 79730
negative_passages.text: $G$ is a planar, connected graph. Let $n$ be number of vertices, $m$ number of edges and $f$ number of faces. Prove that dual graph $G*$ has $f(G*)=n$
negative_passages.docid: 27373
negative_passages.text: Graph Proof by induction.
negative_passages.docid: 145818
negative_passages.text: Edges on an even number of Hamilton cycles
negative_passages.docid: 26398
negative_passages.text: Group of even order contains an element of order 2
negative_passages.docid: 100256
negative_passages.text: Proof by induction on a rooted tree with even number of vertices
negative_passages.docid: 138226
negative_passages.text: Finding All n-regular graphs on m vertices
negative_passages.docid: 94838
negative_passages.text: Show that a self-complementary graph contains an odd number of vertices with degree $(n-1)/2$
negative_passages.docid: 83872
negative_passages.text: Isomorphisms for graphs with loops and multiple edges
negative_passages.docid: 59831
negative_passages.text: How to relate combinatorial proof to bipartite graphs?
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: 127277
negative_passages.text: Graph Theory: Tree has at least 2 vertices of degree 1
negative_passages.docid: 60492
negative_passages.text: Why girth of Petersen Graph is five? (Proof)
negative_passages.docid: 99781
negative_passages.text: Proof that any simple connected graph has at least 2 non-cut vertices.
negative_passages.docid: 91134
negative_passages.text: In any finite graph with at least two vertices, there must be two vertices with the same degree
negative_passages.docid: 140114
negative_passages.text: Using Halls Theorem to show Graph contains a perfect matching containing any edge.
negative_passages.docid: 154564
negative_passages.text: Prove that the sum of minimum edge cover and maximum matching is the vertex count