### Abstract

Original language | English |
---|---|

Journal | Combinatorica |

Volume | 34 |

Issue number | 5 |

Pages (from-to) | 547-559 |

ISSN | 0209-9683 |

DOIs | |

Publication status | Published - 2014 |

### Cite this

*Combinatorica*,

*34*(5), 547-559. https://doi.org/10.1007/s00493-014-2899-4

}

*Combinatorica*, vol. 34, no. 5, pp. 547-559. https://doi.org/10.1007/s00493-014-2899-4

**The circumference of the square of a connected graph.** / Brandt, S.; Muttel, J.; Rautenbach, D.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - The circumference of the square of a connected graph

AU - Brandt, S.

AU - Muttel, J.

AU - Rautenbach, D.

N1 - ISI Document Delivery No.: AT7SD Times Cited: 0 Cited Reference Count: 5 Brandt, Stephan Muettel, Janina Rautenbach, Dieter DFG [RA873/5-1] We were supported by the DFG project "Cycle Spectra of Graphs" RA873/5-1. 0 SPRINGER HEIDELBERG HEIDELBERG COMBINATORICA

PY - 2014

Y1 - 2014

N2 - The celebrated result of Fleischner states that the square of every 2-connected graph is Hamiltonian. We investigate what happens if the graph is just connected. For every n a parts per thousand yen 3, we determine the smallest length c(n) of a longest cycle in the square of a connected graph of order n and show that c(n) is a logarithmic function in n. Furthermore, for every c a parts per thousand yen 3, we characterize the connected graphs of largest order whose square contains no cycle of length at least c.

AB - The celebrated result of Fleischner states that the square of every 2-connected graph is Hamiltonian. We investigate what happens if the graph is just connected. For every n a parts per thousand yen 3, we determine the smallest length c(n) of a longest cycle in the square of a connected graph of order n and show that c(n) is a logarithmic function in n. Furthermore, for every c a parts per thousand yen 3, we characterize the connected graphs of largest order whose square contains no cycle of length at least c.

U2 - 10.1007/s00493-014-2899-4

DO - 10.1007/s00493-014-2899-4

M3 - Journal article

VL - 34

SP - 547

EP - 559

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 5

ER -