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The Prime Puzzles and Problems Connection
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there are more (currently 63) conjectures than in Number Theory section of OPG (currently 31). So some of the problems from there are missing here.
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Chords of longest cycles
Do any three longest paths in a connected graph have a vertex in common?
Chromatic number of $\frac{3}{3}$-power of graph
3-Edge-Coloring Conjecture
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