Hamilton Paths in Generalized Petersen Graphs

Mathematics;graph theory;mathematics;combinatorics;Hamilton paths;generalized Petersen graphs

Pensaert, William

University of Waterloo

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

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/1198/1/wpjpensaert2002.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 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.