The Heawood graph and $K_{3,3}$ have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2-factor hamiltonian graph then either G is a circuit or k = 3. Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and $K_{3,3}$ and conjecture that these are the only such graphs.

2-Factor hamiltonian graphs

FUNK, Martin;LABBATE, Domenico;
2003-01-01

Abstract

The Heawood graph and $K_{3,3}$ have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2-factor hamiltonian graph then either G is a circuit or k = 3. Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and $K_{3,3}$ and conjecture that these are the only such graphs.
2003
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/417
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? 21
social impact