On Cayley Digraphs That Do Not Have Hamiltonian Paths. (26th December 2013)

• Record Type: Journal Article
• Authors: Morris, Dave Witte
• Other Names: Xu Jun-Ming Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2013(2013)
• Publication Date: 2013-12-26
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2013/725809
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : We construct an infinite family{ C a y → ( G i ; a i ; b i ) } of connected, 2 -generated Cayley digraphs that do not have hamiltonian paths, such that the orders of the generatorsa i andb i are unbounded. We also prove that ifG is any finite group with| [ G, G ] | ≤ 3, then every connected Cayley digraph onG has a hamiltonian path (but the conclusion does not always hold when| [ G, G ] | = 4 or5 ).