Status Report on the CPA Conjecture

摘要

The CPA (Castagna, Prins, and Alspach) conjecture asserts that the generalized Petersen graph G(n,k) is Hamiltonian if and only if G(n,k) is approximately unequal to G(n,2) where n is identical with 5 mod 6 and n is unequal to 2k = 4l, l > 1. A new technique for constructing Hamilton paths in G(n,k) is reported here and used to rederive the various earlier results of Robertson, Bondy, Simmons, and Slater very succinctly. The method has also been used to show that the CPA conjecture holds for all k less than or equal to 35. (ERA citation 06:021474)