Dear Andrew,

The author of the project I am currently thinking about how to use my theory of regions to solve graph theoretic problems. I had used my theory of regions to prove the four color theorem mathematically a few years back.

claimed that he developed a new approach (theory of regions) to tackle many of the open problems in graph theory (graph -theoretic problems,)

and one of them is the well known four color problem.

See

(1)https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

(2) neilsloane.com/doc/pace2.pdf

(3) math.ucsd.edu/~fan/ep.pdf

(4) www.ics.uci.edu/~theory/269/020125.pdf

Best regards

This is a very good question. In addition to the helpful answer by @ Issam Kaddoura, there is a bit more to add.

For direct access work on graph theory problems here on RG, see

https://www.researchgate.net/topic/Graph-Theory

For a sampler of open problems in graph theory, see

Article Some open problems on graph labelings

For a practical application of graph theory in air traffic control, see

Article A problem in graph theory arising from air traffic control

For open problems in graph colouring, see

Article Graph Coloring: History, results and open problems

More to the point, see Bertrand's Postulate applied to Hamilton Cycles

Article From a Consequence of Bertrand's Postulate to Hamilton Cycles

For a study of polygons with holes and their visibility graphs, see the attached image from

https://arxiv.org/pdf/1804.05105.pdf

thank you for the information 😄, where might you recommend someone to start to acquire an understanding of the problems‘ foundations? If graph theory problems were a course what are the prerequisite knowledge requirements?