@article{brandt2014a,
title = {The circumference of the square of a connected graph},
language = {eng},
author = {Brandt, S. and Muttel, J. and Rautenbach, D.},
journal = {Combinatorica},
volume = {34},
number = {5},
pages = {547-559},
year = {2014},
issn = {14396912, 02099683},
abstract = {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.},
doi = {10.1007/s00493-014-2899-4}
}