query: Proof of the statement 'World is not flat' by graph theory
positive_passages.docid: 150707
positive_passages.text: Prove the statement 'World is not flat'
negative_passages.docid: 97515
negative_passages.text: Is this graph a planar graph or not?
negative_passages.docid: 148934
negative_passages.text: Proof of Archimedes Principle
negative_passages.docid: 127965
negative_passages.text: Graph theory (Graph Connectivity)
negative_passages.docid: 122998
negative_passages.text: number of edges induction proof
negative_passages.docid: 127818
negative_passages.text: How do I prove that a graph is a topological manifold
negative_passages.docid: 117992
negative_passages.text: Help with graph induction proof
negative_passages.docid: 4112
negative_passages.text: How to prove that a simple graph having 11 or more vertices or its complement is not planar?
negative_passages.docid: 15865
negative_passages.text: Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
negative_passages.docid: 141835
negative_passages.text: Rigorous Proof: Circle cannot be embedded into the the real line!
negative_passages.docid: 35458
negative_passages.text: Prove, that graph $G$ has at least $\chi(G)(\chi(G)-1)/2$ edges.
negative_passages.docid: 142861
negative_passages.text: Multipartite graphs which are not planar
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?
negative_passages.docid: 157150
negative_passages.text: Is the maximum degree of a planar graph 5?
negative_passages.docid: 5612
negative_passages.text: How to prove that we are living in a 3+1D world?
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 ...
negative_passages.docid: 38473
negative_passages.text: Checking whether a graph is planar