Hamiltonian Paths in Some Classes of Grid Graphs

Algorithm 1

The Hamiltonian path algorithm for 𝐿-alphabet grid graphs.

  procedure 𝐿_HamiltonianPath(𝐿(𝑚,𝑛),𝑠,𝑡)

1:  if  𝐿 can be stripped then

2:   let 𝑆 be a strip of 𝐿, where 𝑆 is an even-sized rectangular grid graph

3:   𝑃 ← 𝑅_HamiltonianPath(𝐿−𝑆,𝑠,𝑡)

4:   𝐷 ← HamiltonianCycle(𝑆)

5:   return MergeStrip(𝑃,𝐷,𝑠,𝑡)

6:  else

7:   let 𝐿 be split to 𝑅_𝑝 and 𝑅_𝑞

8:   𝑃₁ ← 𝑅_HamiltonianPath(𝑅_𝑝,𝑠,𝑝)

9:   𝑃₂ ← 𝑅_HamiltonianPath(𝑅_𝑞,𝑞,𝑡)

10:   return MergeSplit(𝑃₁,𝑃₂,𝑝,𝑞)

11:  end  if