Hamiltonian Paths in Some Classes of Grid Graphs

Algorithm 4

The Hamiltonian path algorithm for 𝐸-alphabet grid graphs.

  procedure 𝐸_HamiltonianPath(𝐸(𝑚,𝑛),𝑠,𝑡)

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

   𝑅(2𝑚−4,𝑛)

2:  𝑃 ← 𝐸−𝑆_HamiltonianPath(𝐸−𝑆,𝑠,𝑡)

3:  /*𝐸−𝑆 is a 𝐹-alphabet grid graph 𝐹(𝑚,𝑛) or a 𝐶-alphabet grid graph 𝐶(𝑚,𝑛)*/

4:  𝐷 ← HamiltonianCycle(𝑆)

5:  return MergeStrip(𝑃,𝐷,𝑠,𝑡)