Allen, Peter, Böttcher, Julia and Hladky, Jan
(2011)
*Filling the gap between Turan's theorem and Posa's conjecture.*
Journal of the London Mathematical Society, 84 (2).
pp. 269-302.
ISSN 0024-6107

## Abstract

Much of extremal graph theory has concentrated either on finding very small subgraphs of a large graph (Turán-type results) or on finding spanning subgraphs (Dirac-type results). In this paper, we are interested in finding intermediate-sized subgraphs. We investigate minimum degree conditions under which a graph G contains squared paths and squared cycles of arbitrary specified lengths. We determine precise thresholds, assuming that the order of G is large. This extends results of Fan and Kierstead [J. Combin. Theory Ser. B 63 (1995) 55–64] and of Komlós, Sarközy and Szemerédi [Random Structures Algorithms 9 (1996) 193–211] concerning the containment of a spanning squared path and a spanning squared cycle, respectively. Our results show that such minimum degree conditions constitute not merely an interpolation between the corresponding Turán-type and Dirac-type results, but exhibit other interesting phenomena.

Item Type: | Article |
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Official URL: | http://jlms.oxfordjournals.org/ |

Additional Information: | © 2011 London Mathematical Society |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 28 May 2012 14:21 |

Last Modified: | 20 Jan 2020 04:29 |

URI: | http://eprints.lse.ac.uk/id/eprint/44094 |

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