Help:=proc(): print(`Ham(G), IsLegal(G,P)`):end:


#IsLegal(G,P): is the path P feasible in the graph G?
IsLegal:=proc(G,P) local i:

 evalb({seq(member([P[i],P[i+1]],G[2]),i=1..nops(P)-1)}={true}):

end:

with(combinat):
#Ham(G): Inputs a directed graph (in the form [V,E])
#and outputs all Hamiltinian paths
Ham:=proc(G) local V,E,n,S,Sg,i:
V:=G[1]: E:=G[2]:

S:=permute(V):

Sg:={}:

 for i from 1 to nops(S) do
  if IsLegal(G,S[i]) then
     Sg:=Sg union {S[i]}:
  fi:
od:
Sg:
end:


#IsLegalE(G,P): Is the sequence of edges P 
#feasible in the graph G?
IsLegalE:=proc(G,P) local i:

 evalb({seq(evalb(P[i][2]=P[i+1][1]),i=1..nops(P)-1)}={true}):

end:


#EulerB(G): Inputs a directed graph (in the form [V,E])
#and outputs all Eulerian paths by stupid brute force
EulerB:=proc(G) local V,E,n,S,Sg,i:
V:=G[1]: E:=G[2]:

S:=permute(E):

Sg:={}:

 for i from 1 to nops(S) do
  if IsLegalE(G,S[i]) then
     Sg:=Sg union {S[i]}:
  fi:
od:
Sg:
end: