def encode$\_$and$\_$solve$\_$three$\_$coloring$($n$,$ edge$\_$list$)$:

assert n $>=1,$ 'Graph must have at least one vertex'

assert all$(0<=$ i and i $<$ n and $0<=$ j and j $<$ n and i $!=$ j for $($i$,$j$)$ in edge$\_$list $),$ 'Edge list is not well formed'

prob $=$ LpProblem$(\text{'}$Three Color', LpMinimize$)$