skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "Treglown, Andrew"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; ; (, SIAM Journal on Discrete Mathematics)
    Free, publicly-accessible full text available December 31, 2025
  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. 
    more » « less
    Full Text Available 
  3. ; ; (, Journal of Combinatorial Theory, Series B)
    Full Text Available 
  4. ; ; ; (, Combinatorics, Probability and Computing)
    null (Ed.)
    Abstract A perfect K r -tiling in a graph G is a collection of vertex-disjoint copies of the clique K r in G covering every vertex of G . The famous Hajnal–Szemerédi theorem determines the minimum degree threshold for forcing a perfect K r -tiling in a graph G . The notion of discrepancy appears in many branches of mathematics. In the graph setting, one assigns the edges of a graph G labels from {‒1, 1}, and one seeks substructures F of G that have ‘high’ discrepancy ( i.e. the sum of the labels of the edges in F is far from 0). In this paper we determine the minimum degree threshold for a graph to contain a perfect K r -tiling of high discrepancy. 
    more » « less
    Full Text Available 
  5. ; ; ; (, SIAM Journal on Discrete Mathematics)
    null (Ed.)
    Full Text Available