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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
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Collection of conjectures and open problems in graph theory
A list of about 60 algorithmic problems pertaining to trees are given in the paper by Stephen T. Hedetniemi (Wayback Machine, journal website). Some of the discussion in the paper can be extended to q …