Squarepaths and squarecycles in graphs with high minimum degree
Squarepaths and squarecycles in graphs with high minimum degree

Jan Hladky, Charles University, Prague
Fine Hall 322
We investigate under which minimumdegree condition does a graph G contain a squarepath and a squarecycle of a given length. We give precise thresholds, assuming that the order of G is large. This extends results of Fan and Kierstead [J. Combin. Theory Ser. B, 67(2), 167182, 1996] and of Komlos, Sarkozy, and Szemeredi [Random Structures Algorithms, 9(12), 193211, 1996] concerning containment of a spanning squarepath and a spanning squarecycle, respectively. Joint work with P. Allen and J. Bottcher.