query: Graph theory: graph coloring quesiton
positive_passages.docid: 142917
positive_passages.text: Graph vertex chromatic number in a union of 2 sub-graphs
negative_passages.docid: 52056
negative_passages.text: Chromatic Triangles on a $K_{17}$ graph
negative_passages.docid: 126583
negative_passages.text: Coloring points on an n-gon
negative_passages.docid: 128034
negative_passages.text: Problem on Extremal Graphs: three independent paths
negative_passages.docid: 96803
negative_passages.text: Hall's marriage theorem in bipartite graph
negative_passages.docid: 110760
negative_passages.text: Chromatic Polynomial
negative_passages.docid: 131031
negative_passages.text: Q: Proving G is d-colorable
negative_passages.docid: 99806
negative_passages.text: Given an undirected Graph
negative_passages.docid: 155090
negative_passages.text: A graph whose every odd cycle is a triangle is 4-colorable
negative_passages.docid: 77697
negative_passages.text: Motivation for spectral graph theory.
negative_passages.docid: 19807
negative_passages.text: Connected graph with colored edges
negative_passages.docid: 145194
negative_passages.text: Matrix graph and irreducibility
negative_passages.docid: 91253
negative_passages.text: Proving that every graph that each vertex at degree 2 must contain a cycle
negative_passages.docid: 57930
negative_passages.text: Chromatic polynomial properties
negative_passages.docid: 42513
negative_passages.text: Graph with Cycle and Two-Colorable
negative_passages.docid: 115085
negative_passages.text: number of vertices in a self-complemntary graph
negative_passages.docid: 8458
negative_passages.text: Combinatorics problem based on Ferrers graph