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Creators/Authors contains: "Krueger, Robert A"

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  1. ; ; ; ; ; ; ; (, Discrete & Computational Geometry)
    Free, publicly-accessible full text available March 1, 2026
  2. ; ; ; ; (, Combinatorics, Probability and Computing)
    Abstract In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every$$\alpha \gt 0$$, there exists a constant$$C$$such that for every$$n$$-vertex digraph of minimum semi-degree at least$$\alpha n$$, if one adds$$Cn$$random edges then asymptotically almost surely the resulting digraph contains a consistently oriented Hamilton cycle. We generalize their result, showing that the hypothesis of this theorem actually asymptotically almost surely ensures the existence of every orientation of a cycle of every possible length, simultaneously. Moreover, we prove that we can relax the minimum semi-degree condition to a minimum total degree condition when considering orientations of a cycle that do not contain a large number of vertices of indegree$$1$$. Our proofs make use of a variant of an absorbing method of Montgomery. 
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  3. ; ; (, Random Structures & Algorithms)
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  4. ; ; ; (, Journal of Graph Theory)