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.

Original language | English |
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Place of Publication | Enschede |
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Publisher | University of Twente |
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Number of pages | 21 |
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Publication status | Published - 2002 |
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Name | Hamburger Beiträge zur Mathematik |
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Publisher | University of Hamburg |
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No. | 152 |
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