#ClosestEligibleMatches(k,f,i): 
#given an fpl f of size k, and i in [1,2k], finds the
#shortest  eligible match to be e_i(f)
#For example, try:
#ClosestEligibleMatches(3,FPL(3)[1],1);
ClosestEligibleMatches:=proc(k,f,i) local gu,shi,mu,g:
gu:=EligibleMatches(k,f,i):

if gu={} then 
RETURN(FAIL):
fi:

shi:=min(seq(g[2], g in gu)):

mu:={}:

for g in gu do
 if g[2]=shi then
  mu:=mu union {g[1]}:
 fi:
od:
mu:


end:



#PathFrom(k,P1,f): Given a point P1 in [0,k+1]^2
#with degree 1, and an fpl f,
#finds the path that starts with P1.
#For example, try: 
#PathFrom(3,[1,0],FPL(3)[1]);
PathFrom:=proc(k,P1,P2,f) local T,edg, i,j,lu:
option remember:


for i from 0 to k+1 do
 for j from 0 to k+1 do
  T[[i,j]]:={}:
 od:
od:

for edg in f do
 T[edg[1]]:=T[edg[1]] union {edg[2]}:
 T[edg[2]]:=T[edg[2]] union {edg[1]}:
od:

if nops(T[P1])<>1 then
 RETURN(FAIL):
fi:


gu:=[P1]:

lu:=T[P1][1]:

while nops(T[lu])=2 do
 gu:=[op(gu),lu]:
 lu:=(T[lu] minus {lu})[1]:
od:
gu:
end: