offering powerful new methods to address long-standing conjectures in graph theory [3]. Planar Graph: A graph that can be drawn on a plane without any edges crossing. Graph Colouring: The process ...

The two rushed to draft a new paper. They presented it in June at the ACM Symposium on Theory of Computing, where they detailed an exponentially better method for checking whether a graph is planar.

Correction April 20, 2018: The original version of this article reported that de Grey had found a “planar unit-distance graph.” In graph theory, “planar” means that a graph can be embedded in the ...

Additionally, research on planar graphs has yielded new insights into the anti-Ramsey numbers for paths and cycles, thereby bridging classical graph theory with geometric constraints [3].

Problem 1: Find a subquadratic algorithm for testing if a given graph is 1-planar. It is also easy to check in cubic ... This follows from Robertson and Seymour's theory of graph minors since the ...

This is the case with an important problem in computer science called "graph isomorphism testing" whereby scientists use ...

Agnes M. Herzberg and M. Ram Murty of Queen’s University in Kingston, Ontario have translated the problem of solving a sudoku puzzle into the language of graph theory. The 81 squares in the grid ...