query: Property of simple bipartite graphs
positive_passages.docid: 25382
positive_passages.text: Maximum number of edges in a bipartite graph
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: 49585
negative_passages.text: Proof a graph is bipartite if and only if it contains no odd cycles
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: 35418
negative_passages.text: Equivalent definitions for simple connectivity
negative_passages.docid: 108417
negative_passages.text: Cycles of length k in a complete simple graph with n vertices
negative_passages.docid: 146933
negative_passages.text: Proving bipartition in a connected planar graph
negative_passages.docid: 150508
negative_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: 83872
negative_passages.text: Isomorphisms for graphs with loops and multiple edges
negative_passages.docid: 91253
negative_passages.text: Proving that every graph that each vertex at degree 2 must contain a cycle
negative_passages.docid: 142917
negative_passages.text: Graph vertex chromatic number in a union of 2 sub-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: 117707
negative_passages.text: d-regular bipartite graph
negative_passages.docid: 92609
negative_passages.text: How to Mathematically Prove the Bilinear Pairing Properties
negative_passages.docid: 127277
negative_passages.text: Graph Theory: Tree has at least 2 vertices of degree 1
negative_passages.docid: 138465
negative_passages.text: Graph Coloring and Complete Graph
negative_passages.docid: 48692
negative_passages.text: A problem about the graph theory