### Research

random graph theory, random graph processes, analysis of randomized algorithms and stochastic processes

### Publications

- P. Gao and C. M. Sato, "Change of limiting distributions of large matchings in random graphs", preprint available on arXiv.
- P. Gao, X. Perez-Gimenez and C. M. Sato, "Arboricity and spanning-tree packing of random graphs", preprint available on arXiv.
- P. Gao, "Sandwiching the densest subgraph by consecutive cores", submitted.
- P. Gao, "On the geometric Ramsey numbers of trees", submitted.
- E. Ebrahimzade, F. Farczadi, P. Gao, A. Mehrabian, C. Sato, N. Wormald and J. Zung, "On the longest path and the diameter in random Apollonian networks", submitted, preprint available on arXiv.
- P. Gao, "The first $k$-regular subgraph is large", submitted, preprint available on arXiv.
- P. Gao, N. C. Wormald, "Orientability thresholds of random hypergraphs", submitted, preprint available on arXiv.
- P. Gao, "Uniform generation of $d$-factors in dense host graphs", Graphs and Combinatorics, 2012, accepted.
- P. Gao, "Distributions of sparse spanning subgraphs in random graphs", SIAM Journal on Discrete Mathematics, 2012, accepted.
- P. Gao, "Distribution of the number of spanning regular subgraphs in random
graphs", Random Struct. Algorithms, DOI: 10.1002/rsa.20418.
- P. Gao, Y. Su and N. C. Wormald, "Induced subgraphs in sparse random graphs with given degree
sequence", European Journal of Combinatorics, 33(6): 1142--1166 (2012).
- P. Gao, N. C. Wormald, "Load balancing and orientability thresholds for random hypergraphs", STOC 2010.
- P. Gao, "The connectivity of the random regular graphs generated by the pegging algorithm",J. Graph Theory, 65(3), 185--197, 2010.
- P. Gao, N. C. Wormald, "Rate of convergence of the short cycle distribution in random regular graphs generated by pegging", Elec. J. Combinatorics, Volumn 16(1)(2009), R44, 17 pp.
- P. Gao, N. C. Wormald, "Short cycle distributions in random regular graphs recursively generated by pegging", Random Struct. Algorithms 34(1): 54-86 (2009)