This is inspired by the similar question on modern set theory. I've read through the open problems in graph theory on Wikipedia's list of unsolved problems in mathematics, but what I'm looking for is more an accessible description of the main areas of graph theoretical research. I hope this is okay to ask.
2026-03-25 06:02:18.1774418538
What are the big issues in modern graph theory?
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The biggest one and the most simple one is the absence of a necessary and sufficient condition for a graph to be Hamiltonian. There are a few sufficient conditions (as far as I know) but all of them are pretty weak - or require strong conditions. The simplicity of Eulerian paths in graphs and the complexity of Hamiltonian paths is fascinating. And if I'm right this is one of the biggest problems in Graph Theory right now.