Good Will Hunting Problems

The second blackboard problem in the 1997 film Good Will Hunting asks for all the series-reduced trees (referred to by the alternate term "homeomorphically irreducible trees" in the film) on 10 nodes. Here, "series-reduced" means there are no vertices of degree 2 so that a topologically equivalent structure can be obtained by merging two incident edges at a vertex (i.e., no node merely allows a single edge to "pass through"). There are exactly 10 such trees, illustrated above (though only eight of them are drawn by the character Will in the film).

REFERENCES

Horváth, G.; Korándi, J.; and Szabò, C. "Mathematics in Good Will Hunting II: Problems from the Students Perspective." Teach. Math. Comput. Sci. 11, No. 1, 3-19, 2013.

Koraándi, J. and Pluhàr, G. "Mathematics and Good Will Hunting I." Teach. Math. Comput. Sci. 10, No. 2, 375Ð388, 2012.

StackExchange: Mathematica & Wolfram Language. "List All Homeomorphically Distinct Irreducible Connected Acyclic Graphs of Size 10 ('Good Will Hunting' Problem)." Mar. 25-26, 2022. https://mathematica.stackexchange.com/questions/265641/list-all-homeomorphically-distinct-irreducible-connected-acyclic-graphs-of-size.

Veisdal, J. "The Math Problems from Good Will Hunting, w/ Solutions." Jul. 31, 2019. https://www.cantorsparadise.com/the-math-problems-from-good-will-hunting-w-solutions-b081895bf379.