Now, more than 122 years after it was first proposed, Kamata and two other mathematicians have finally proved that a solution ...

From here graph theory got expanded and generalized into ... By preprocessing the graph, unimportant vertices (intersections) and edges can be skipped, leading to a major speed-up.

In graph theory, a graph is a network of lines, called edges, and points where they meet, called vertices. After 122 years, a team of mathematicians has finally solved the puzzle. They proved that ...

But in theory ... of each node in the graph and assigns it a color. The different colors thus assigned allow the algorithm to easily identify how many other vertices a particular node "sees." ...

Yet it’s been proven that if you have a graph with a certain set of vertices, coloring the resulting lines in this manner will always result in a clique forming. This phenomenon has been ...