An algorithm for finding Hamiltonian Cycles in Cubic Planar Graphs

TL;DR

This paper introduces an exact algorithm with exponential worst-case complexity for finding Hamiltonian cycles in cubic planar graphs by leveraging a novel correspondence with certain trees in dual graphs.

Contribution

The paper establishes a new correspondence between Hamiltonian cycles in cubic planar graphs and specific trees in their dual graphs, leading to an exact algorithm.

Findings

Proves a one-to-one correspondence between Hamiltonian cycles and certain trees in dual graphs.

Constructs an exact algorithm with O(2^n) complexity for the problem.

Provides theoretical foundation for future algorithmic improvements.

Abstract

We first prove a one-to-one correspondence between finding Hamiltonian cycles in a cubic planar graphs and finding trees with specific properties in dual graphs. Using this information, we construct an exact algorithm for finding Hamiltonian cycles in cubic planar graphs. The worst case time complexity of our algorithm is O$(2^n)$.