The circumference of the square of a connected graph

Research output: Contribution to journalJournal article

View graph of relations

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.
LanguageEnglish
JournalCombinatorica
Volume34
Issue number5
Pages (from-to)547-559
ISSN0209-9683
DOIs
StatePublished - 2014