Research / Publications

Last updated 17 Jan 2017.

Papers

• B. Bukh, P. Loh, and G. Nivasch, Classifying unavoidable Tverberg partitions, submitted.
• P. Loh, M. Tait, and C. Timmons, Induced Turan numbers, submitted.
• J. Briggs, A. Frieze, M. Krivelevich, P. Loh, and B. Sudakov, Packing Hamilton cycles online, submitted.
• P. Loh, Directed paths: from Ramsey to Ruzsa and Szemerédi, Combinatorics, Probability and Computing, to appear.
• P. Loh and S. Oh, Cops and robbers on planar directed graphs, Journal of Graph Theory, to appear.
• P. Loh and J. Ma, Diameter critical graphs, Journal of Combinatorial Theory, Series B, 117 (2016), 34-58.
• M. Lavrov and P. Loh, Hamiltonian increasing paths in random edge orderings, Random Structures and Algorithms, 48 (2016), 588-611.
• C. Lee, P. Loh, and B. Sudakov, Judicious partitions of directed graphs, Random Structures and Algorithms, 48 (2016), 147-170.
• W. Gan, P. Loh, and B. Sudakov, Maximizing the number of independent sets of a fixed size, Combinatorics, Probability and Computing, 24 (2015), 521-527.
• J. Fox, P. Loh, and Y. Zhao, The critical window for the classical Ramsey-Turan problem, Combinatorica, 35 (2015), 435-476.
• J. Iglesias, N. Ince, and P. Loh, Computing with voting trees, SIAM Journal on Discrete Mathematics, 28 (2014), 673-684.
• P. Loh and R. Pagh, Thresholds for extreme orientability, Algorithmica, 69 (2014), 522-539.
• D. Bal, A. Frieze, M. Krivelevich, and P. Loh, Packing tree factors in random and pseudo-random graphs, The Electronic Journal of Combinatorics, 21 (2014), P2.8.
• A. Frieze and P. Loh, Rainbow Hamilton cycles in random graphs, Random Structures and Algorithms, 44 (2014), 328-354.
• R. Graham, L. Hamilton, A. Levavi, and P. Loh, Anarchy is free in network creation, Proc. 10th Workshop on Algorithms and Models for the Web Graph, LNCS 8305 (2013), 220-231.
• C. Lee, P. Loh, and B. Sudakov, Bisections of graphs, Journal of Combinatorial Theory, Series B, 103 (2013), 599-629.
• C. Lee, P. Loh, and B. Sudakov, Self-similarity of graphs, SIAM Journal on Discrete Mathematics, 27 (2013), 959-972.
• P. Loh and E. Lubetzky, Stochastic coalescence in logarithmic time, Annals of Applied Probability, 23 (2013), 492-528.
  This version appeared in the proceedings of SODA 2012, pages 541-550.
• J. Fox and P. Loh, On a problem of Erdős and Rothschild on edges in triangles, Combinatorica, 32 (2012), 619-628.
• A. Dudek, A. Frieze, P. Loh, and S. Speiss, Optimal divisibility conditions for loose Hamilton cycles in random hypergraphs, The Electronic Journal of Combinatorics, 19 (2012), P44.
• A. Frieze, M. Krivelevich, and P. Loh, Packing tight Hamilton cycles in 3-uniform hypergraphs, Random Structures and Algorithms, 40 (2012), 269-300.
  This version appeared in the proceedings of SODA 2011, pages 913-932.
• H. Huang, P. Loh, and B. Sudakov, The size of a hypergraph and its matching number, Combinatorics, Probability and Computing, 21 (2012), 442-450.
• A. Frieze, M. Krivelevich, and P. Loh, Variations on Cops and Robbers, Journal of Graph Theory, 69 (2012), 383-402.
• T. Bohman, A. Frieze, M. Krivelevich, P. Loh, and B. Sudakov, Ramsey games with giants, Random Structures and Algorithms, 38 (2011), 1-32.
• P. Loh, O. Pikhurko, and B. Sudakov, Maximizing the number of q-colorings, Proceedings of the London Mathematical Society, 101 (2010), 655-696.
• P. Loh, A note on embedding hypertrees, The Electronic Journal of Combinatorics, 16 (2009), N18.
• P. Loh and B. Sudakov, Constrained Ramsey Numbers, Combinatorics, Probability and Computing, 18 (2009), 247-258.
• J. Fox, P. Loh, and B. Sudakov, Large induced trees in K_r-free graphs, Journal of Combinatorial Theory, Series B, 99 (2009), 494-501.
• M. Krivelevich, P. Loh, and B. Sudakov, Avoiding small subgraphs in Achlioptas processes, Random Structures and Algorithms, 34 (2009), 165-195.
  The unabridged version is on the arXiv.
• P. Loh and B. Sudakov, On the strong chromatic number of random graphs, Combinatorics, Probability and Computing, 17 (2008), 271-286.
• P. Loh and B. Sudakov, Independent transversals in locally sparse graphs, Journal of Combinatorial Theory, Series B, 97 (2007), 904-918.
• P. Keevash, P. Loh, and B. Sudakov, Bounding the number of edges in permutation graphs, The Electronic Journal of Combinatorics, 13 (2006), R44.
• P. Loh and L. Schulman, Improved expansion of random Cayley graphs, Discrete Mathematics and Theoretical Computer Science, 6 (2004), 523-528.
• P. Loh, Finding shortest paths with computational geometry, Journal of Graph Algorithms and Applications, 7 (2003), 287-303.

Olympiad related

• P. Loh, 57th International Mathematical Olympiad , Mathematics Magazine, 89 (2016), 388-397.
• P. Loh, 56th International Mathematical Olympiad , Mathematics Magazine, 88 (2015), 305-315.
• P. Loh, 55th International Mathematical Olympiad , Mathematics Magazine, 87 (2014), 310-317.
• Z. Feng, P. Loh, and Y. Sun, 51st International Mathematical Olympiad, Mathematics Magazine, 83 (2010), 320-323.
• Eds. T. Andreescu, Z. Feng, and P. Loh, USA and International Mathematical Olympiads 2004, published by the Mathematical Association of America (2005), 100pp.

Slides (research)

• M. Lavrov and P. Loh, Hamilton increasing paths in random edge orderings.
• C. Lee, P. Loh, B. Sudakov, Judicious bisections.
• J. Fox, P. Loh, Edges and triangles.
• A. Frieze, P. Loh, Rainbow Hamilton cycles in random graphs.
• A. Frieze, M. Krivelevich, P. Loh, Packing tight Hamilton cycles.
• P. Loh, E. Lubetzky, Stochastic coalescence.
• A. Frieze, M. Krivelevich, P. Loh, Variations on Cops and Robbers.
• T. Bohman, A. Frieze, M. Krivelevich, P. Loh, B. Sudakov, Ramsey games with giants.
• J. Fox, P. Loh, B. Sudakov, Large induced trees in K_r-free graphs.
• P. Loh, O. Pikhurko, B. Sudakov, Maximizing the number of colorings.
• M. Krivelevich, P. Loh, B. Sudakov, Avoiding small subgraphs in Achlioptas processes.
• P. Loh, B. Sudakov, Constrained Ramsey numbers.
• P. Loh, B. Sudakov, Independent transversals in locally sparse graphs.
• P. Loh, Random Cayley graphs and the second eigenvalue problem.

Slides (expository)

• Using uncertainty to establish certainty, invited talk showcasing the Fall 2009 IPAM Program on Combinatorics at the Math Institutes Modern Mathematics Workshop, 2008 SACNAS* National Conference.