## Abstract

A graph G is collapsible if for every even subset X ⊆ V (G), G has a subgraph Γ such that G - E (Γ) is connected and the set of odd-degree vertices of Γ is X. A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G. In this paper, we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between the line graph of the reduction and the reduction of the line graph. Our results extend former results in [H.-J. Lai, Reduced graph of diameter two, J. Graph Theory 14 (1) (1990) 77-87], and in [P.A. Catlin, Iqblunnisa, T.N. Janakiraman, N. Srinivasan, Hamilton cycles and closed trails in iterated line graphs, J. Graph Theory 14 (1990) 347-364].

Original language | English |
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Pages (from-to) | 3173-3184 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 10 |

DOIs | |

Publication status | Published - 28 May 2009 |

## Scopus Subject Areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## User-Defined Keywords

- Collapsible graph
- Double cycle covers
- Hamiltonian index
- Line graphs
- Reduction of graph