Hamilton Paths in Generalized Petersen Graphs

[摘要] This thesis puts forward the conjecture that for n > 3k with k > 2, the generalized Petersen graph, GP(n,k) is Hamilton-laceable if n is even and k is odd, and it is Hamilton-connected otherwise.We take the first step in the proof of this conjecture by proving the case n = 3k + 1 and k greater than or equal to 1.We do this mainly by means of an induction which takes us from GP(3k + 1, k) to GP(3(k + 2) + 1, k + 2).The induction takes the form of mapping a Hamilton path in the smaller graph piecewise to the larger graph an inserting subpaths we call rotors to obtain a Hamilton path in the larger graph.

[发布机构] University of Waterloo

[效力级别] graph theory

[关键词] Mathematics;graph theory;mathematics;combinatorics;Hamilton paths;generalized Petersen graphs