%AAnastos, Michael [Institut für Mathematik Freie Universität Berlin Berlin Germany]%AFrieze, Alan [Department of Mathematical Sciences Carnegie Mellon University Pittsburgh Pennsylvania]%BJournal Name: Random Structures & Algorithms; Journal Volume: 57; Journal Issue: 4; Related Information: CHORUS Timestamp: 2023-09-04 16:02:48
%D2020%IWiley Blackwell (John Wiley & Sons)
%JJournal Name: Random Structures & Algorithms; Journal Volume: 57; Journal Issue: 4; Related Information: CHORUS Timestamp: 2023-09-04 16:02:48
%K
%MOSTI ID: 10260105
%PMedium: X
%THamilton cycles in random graphs with minimum degree at least 3: An improved analysis
%XIn this paper we consider the existence of Hamilton cycles in the random graph. This random graph is chosen uniformly from, the set of graphs with vertex set [n],medges and minimum degree at least 3. Our ultimate goal is to prove that ifm = cnandc > 3/2 is constant thenGis Hamiltonian w.h.p. In Frieze (2014), the second author showed thatc ≥ 10 is sufficient for this and in this paper we reduce the lower bound toc > 2.662…. This new lower bound is the same lower bound found in Frieze and Pittel (2013) for the expansion of so‐called Pósa sets.

%0Journal Article