Hamiltonian Paths in Some Classes of Grid Graphs

Algorithm 2

The Hamiltonian path algorithm for 𝐶-alphabet grid graphs.

  procedure 𝐶_HamiltonianPath(𝐶(𝑚,𝑛),𝑠,𝑡)

1:  if  𝐶 can be stripped then

2:   let 𝑆 be a strip of 𝐶, where 𝑆 is an even-sized rectangular grid graph 𝑅(2𝑚−2,𝑛)

3:   𝑃 ← 𝐿_HamiltonianPath(𝐶−𝑆,𝑠,𝑡)

4:   𝐷 ← HamiltonianCycle(𝑆)

5:   return MergeStrip(𝑃,𝐷,𝑠,𝑡)

6:  else

7:   let 𝐶 be split 𝑅_𝑝 and 𝐿_𝑞

8:   𝑃₁ ← 𝑅_HamiltonianPath(𝑅_𝑝,𝑠,𝑝)

9:   𝑃₂ ← 𝐿_HamiltonianPath(𝐿_𝑞,𝑞,𝑡)

10:  return MergeSplit(𝑃₁,𝑃₂,𝑝,𝑞)

11:  end  if