Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f(k) vertices whenever k ≤ (n−f(k))/2. This is a common generalization of vertex connectivity (when f is constant) and expansion (when f is linear). We show that an f-connected graph contains a cycle of length linear in n if f is any linear function, contains a 1-factor and a 2-factor if f(k) ≥ 2k + 1, and contains a Hamilton cycle if f(k) ≥ 2(k + 1)2. We conjecture that linear growth of f suffices to imply hamiltonicity.
|Place of Publication||Enschede|
|Publisher||University of Twente|
|Number of pages||21|
|Publication status||Published - 2002|
|Name||Hamburger Beiträge zur Mathematik|
|Publisher||University of Hamburg|