Graphs with no 𝐾_𝟑,𝟑 Minor Containing a Fixed Edge

Algorithm 1

Algorithm  ford-fulkerson;

begin

  𝐻∶=𝐺;

  𝐷∶={𝑒};

  while  𝐷 does not contain an 𝑒-cut of 𝐻  do

    begin

     set 𝑃 to be an admissible 𝑒-path of 𝐻;

     𝜖∶=min{𝑐_𝑓∣𝑓∈𝑃};

     𝑐_𝑓∶=𝑐_𝑓−𝜖 for 𝑓∈𝑃;

     choose 𝑓∈𝑃 such that 𝑐_𝑓=0 and set 𝐻←𝐻⧵𝑓;

     𝐷←𝐷∪{𝑓};

    end;

end;