4-ordered hamiltonicity for some chordal ring graphs

David Sherman, Ming Tsai, Cheng Kuan Lin, László Lipták, Eddie Cheng, Jimmy J.M. Tan, Lih Hsing Hsu

Research output: Contribution to journalArticlepeer-review

Abstract

A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an infinite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997 by Ng and Schultz. At the time, the only known examples were K4 and K3,3. Some progress was made in 2008 by Mészáros, when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover, an infinite class of 3-regular 4-ordered graphs was found. In 2010 a subclass of generalized Petersen graphs was shown to be 4-ordered by Hsu et al., with an infinite subset of this subclass being 4-ordered Hamiltonian, thus answering the open question. In this paper we find another infinite class of 3-regular 4-ordered Hamiltonian graphs, part of a subclass of the chordal ring graphs. In addition, we classify precisely which of these graphs are 4-ordered Hamiltonian.

Original languageEnglish (US)
Pages (from-to)157-174
Number of pages18
JournalJournal of Interconnection Networks
Volume11
Issue number3-4
DOIs
StatePublished - 2010

Bibliographical note

Funding Information:
∗Research partially supported by the NSF-REU Grant DMS 0649099. †Research partially supported by the NSF-REU Grant DMS 0649099. ‡Corresponding author. Research partially supported by the NSF-REU Grant DMS 0649099.

Keywords

  • 4-ordered
  • Chordal ring graphs
  • Hamiltonian

Fingerprint Dive into the research topics of '4-ordered hamiltonicity for some chordal ring graphs'. Together they form a unique fingerprint.

Cite this