Hamilton Paths in Grid Graphs

Abstract

A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes. In contrast, the Hamilton path (and circuit) problem for general grid graphs is shown to be NP-complete. This provides a new, relatively simple, proof of the result that the Euclidean traveling salesman problem is NP-complete.

DOI: 10.1137/0211056

Extracted Key Phrases

Showing 1-10 of 15 references

Hamiltonian paths on a rectangular chessboard

  • Lm ] F Luccio, C Mugnai
  • 1978

Linear and planar arrangements of graphs

  • Y Shiloach
  • 1976

Case 2. n =2, m =3

Case 3. n 3 (Fig. 3.5b) Without loss of generality s is white. The edge pq (2, 1)(3, 1) splits (R, s, t) q since q is white and is black

Showing 1-10 of 165 extracted citations
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