Comment Comment by gexaha Nice puzzle, congrats! I also like this part of maths, and there's a related concept of Snark graphs.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 parent gexaha 2 years ago
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