, Volume 34, Issue 5, pp 547–559 | Cite as

The circumference of the square of a connected graph

  • Stephan Brandt
  • Janina Müttel
  • Dieter Rautenbach
Original Paper


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 ≥ 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 ≥ 3, we characterize the connected graphs of largest order whose square contains no cycle of length at least c.

Mathematics Subject Classification (2000)

05C38 05C76 05C05 


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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Stephan Brandt
    • 1
  • Janina Müttel
    • 2
  • Dieter Rautenbach
    • 2
  1. 1.Department of Mathematics and Computer Science (IMADA)University of Southern DenmarkOdenseDenmark
  2. 2.Institut für Optimierung und Operations ResearchUniversität UlmUlmGermany

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