2023/05/04 by Gessel, Ira M. · 1 citation
#05A15 (Secondary) #05C30 (Primary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.03157
In the film Good Will Hunting, the main character, a janitor at MIT named Will Hunting, attacks the problem of drawing all the homeomorphically irreducible trees with 10 vertices. Although the film suggests that this is a difficult problem, it is in fact quite easy. A much more interesting problem is counting homeomorphically irreducible trees with n vertices for all n, a feat accomplished by Harary and Prins in 1959. Here we give an exposition and simplification of Harary and Prins's result, introducing some of the fundamental ideas of graphical enumeration.