gexaha

https://en.wikipedia.org/wiki/Snark_(graph_theory)

First is that "One of the equivalent forms of the four color theorem is that every snark is a non-planar graph". Second, is as strengthened form of the four color theorem: "every snark has the Petersen graph as a minor", which is kind of proven (already 25 years ago), but still lacks 1 paper: https://thomas.math.gatech.edu/FC/generalize.html https://math.stackexchange.com/questions/3692582/what-is-the...

And another related concept is of nowhere-zero flows, and even more stronger conjecture that "every bridgeless graph with no Petersen minor has a nowhere zero 4-flow". https://en.wikipedia.org/wiki/Nowhere-zero_flow