My research is currently supported by the Simons Foundation through the Travel Support for Mathematicians program (SFI-MPS-TSM-00024413) for the period  September 1, 2026 to August 31, 2031. Previous support was provided by the National Science Foundation under Grants DMS-2153945 and DMS-1854903,  and by the National Security Agency under Grant H98230-09-1-0055.

My current research interests primarily focus on Hadwiger’s Conjecture and its strengthenings and weakenings; Ramsey related problems including size of co-critical graphs and Ramsey numbers of graphs; and the Erdos-Lovasz Tihany Conjecture.

Preprints 

• On the size of (Kt1, .. Ktk)-co-critical graphs, arXiv:2608.07422
• The Erdos-Lovasz Tihany Conjecture holds for all even-hole-free graphs, arXiv:2607.20376
• Dominating Hadwiger’s Conjecture holds for all 2K2-free graphs (with undergraduate student Thomas Tibbetts), arXiv:2510.12567
• Dominating Hadwiger’s Conjecture for graphs with independence number two (with PhD student Michael Scully), arXiv:2510.12564
• Odd clique minors in graphs with independence number two (with Yuqing Ji, Xia Zhang and undergraduate student Evan Weiss), submitted.  arXiv:2505.07727
• Multicolor bipartite Ramsey number of double stars (with undergraduate student Gregory DeCamillis), submitted.   arXiv:2312.03670
• The minimum degree of (Ks,Kt)-co-critical graphs (with undergraduate students Ivan Casas-Rocha and Benjamin Snyder), submitted.  arXiv:2311.04800
• Every graph with no K8-4e minor is 7-colorable (with PhD student Michael Lafferty), submitted. arXiv:2208.07338
• Every graph with no K9-6e minor is 8-colorable (with PhD student Michael Lafferty), submitted. arXiv:2209.05259
• An improved lower bound for the Planar Turan number of cycles (with Yongxin Lan), submitted. arXiv:2209.01312
• Improved upper bounds for Gallai-Ramsey numbers of odd cycles  (with PhD students Christian Bosse, Jingmei Zhang),  preprint 2018.  arXiv:1808.09963
• Multicolor Gallai-Ramsey numbers of C9 and C11 (with PhD student Christian Bosse), preprint 2018,  arXiv:1802.06503. 

Journal Publications

• Breaking the degeneracy barrier for coloring graphs with no Kt minor (with Sergey Norin and Luke Postle), Advances in Mathematics 422 (2023), 109020.
• A new upper bound for the chromatic number of graphs with no odd Kt minor (with Sergey Norin), Combinatorica 42 (2022) 137–149.
• On tight (k,ell)-stable graphs (with Xiaonan Liu and Zhiyu Wang), to appear in Journal of Graph Theory.
• Minimizing the edges in (C4,star)-co-critical graphs (with Gang Chen and Chenchen Ren), Discrete Mathematics 348 (2025), 114409.
• Multicolor Ramsey number for double stars (with undergraduate student Jake Ruotolo), Discrete Mathematics 347 (2024), 114034.
• Planar Turan numbers of cubic graphs and disjoint union of cycles (with Yongxin Lan and  Yongtang Shi),  Graphs and Combinatorics 40 (2024), article number 28.
• Properties of 8-contraction-critical graphs with no K7 minor (with PhD student Martin Rolek,  Robin Thomas),  European Journal of Combinatorics 110 (2023), 103711.
• A note on odd colorings of 1-planar graphs (with Dan Cranston and PhD student Michael Lafferty), Discrete Applied Mathematics 330 (2023) 112-117.
• Gallai-Ramsey number of odd cycles with chords (with Yaojun Chen,  Fangfang Zhang),  European Journal of Combinatorics 107 (2023), 103598.
• Some remarks on even-hole-free graphs,  The Electronic Journal of Combinatorics 29 (2022), P3.30.
• On the size of (Kt, path)-co-critical graphs (with Gang Chen, Zhengke Miao,  PhD student Jingmei Zhang), Graphs and Combinatorics 38 (2022), 136.
• On the size of (Kt,star)-co-critical graphs (with undergraduate student Hunter Davenport,   Fan Yang),  European Journal of Combinatorics 104 (2022), 103533.
• The Erdos-Lovasz Tihany Conjecture — a survey,  Advances in Mathematics (China)(数学进展）51 (2022) 259–274.
• Gallai-Ramsey number of even cycles with chords (with Yaojun Chen,  Fangfang Zhang), Discrete Mathematics 345 (2022), 112738.
• A survey on planar Turan and anti-Ramsey number of graphs (with Yongxin Lan, Yontang Shi), Operations Research Transactions (运筹学学报) 25 (2021) 200–216.
• On the size of special class 1 graphs and (P3;k)-co-critical graphs (with Gang Chen, Zhengke Miao,  PhD student Jingmei Zhang),  Discrete Mathematics 344 (2021), 112604.
• On the size of (Kt, Tk)-co-critical graphs (with PhD student Jingmei Zhang),   The Electronic Journal of Combinatorics 28(1) (2021), #P1.13.
•  Multicolor Gallai-Ramsey numbers of C10 and C12 (with Hui Lei, Yongtang  Shi,  PhD student Jingmei Zhang),  Australian Journal of Combinatorics 79 (2021) 380-400.
• Antimagic orientations of graphs with given independence number (with Donglei Yang, Fangfang Zhang),  Discrete Applied Mathematics, 291 (2021) 163-170.
• Antimagic orientations of graphs with large maximum degree (with D. Yang, J. Carlson, A. Owens, K. Perry, I. Singgih, F. Zhang, X. Zhang),  Discrete Mathematics 343 (2020)  112123.
• A note on Gallai-Ramsey number of even wheels (with Bing Wei, Fangfang Zhang, Qinghong Zhao), Discrete Mathematics 343 (2020) 111725.
• Some remarks on interval colorings of complete tripartite and biregular graphs (with Puning Jing, Zhengke Miao),  Discrete Applied Mathematics 277 (2020) 193-197.
• Antimagic orientations of even regular graphs (with Tong Li, Guanghui Wang, Donglei Yang, C-Q. Zhang),  J. Graph Theory 90 (2019) 45-53.
• Extremal H-free planar graphs (with Yongxin Lan, Yongtang  Shi),  Electronic Journal of Combinatorics 26 (2019) #P2.
• A conjecture on Gallai-Ramsey numbers of even cycles and paths  (with PhD student  Jingmei Zhang ), Australasian Journal of Combinatorics 75 (2019) 296-308.
• Erdos-Lovasz Tihany Conjecture for graphs with forbidden holes, Discrete Mathematics  342 (2019) 2632-2635.
• Extremal Theta-free planar graphs  (with Yongxin Lan, Yongtang Shi), Discrete Mathematics 342 (2019) 111610.
• Planar anti-Ramsey numbers of paths and cycles  (with Yongxin Lan, Yongtang Shi), Discrete Mathematics 342 (2019) 3216-3224.
• Planar anti-Ramsey numbers of matchings (with Gang Chen and Yongxin Lan), Discrete Mathematics 342 (2019) 2106-2111.
• Gallai-Ramsey numbers of C7 with multiple colors (with undergraduate student Dylan Bruce),  Discrete Mathematics 342 (2019) 1191-1194.
• Star chromatic index of subcubic multigraphs (with Hui Lei, Yongtang Shi), J. Graph Theory  88 (2018) 566-576.
• Clique minors in double-critical graphs (with PhD student Martin Rolek), J. Graph Theory 88 (2018) 347-355.
• Saturation numbers of Ramsey-minimal graphs (with PhD student Martin Rolek),  Discrete Mathematics 341 (2018) 3310-3320.
• Star 5-edge-colorings of subcubic multigraphs (with Hui Lei, Yongtang Shi,  Tao Wang),   Discrete Mathematics 341 (2018) 950-956.
• Coloring graphs with forbidden minors (with PhD student Martin Rolek),  J. Combinatorial Theory, Ser. B 127 (2017) 14-31.
• Hadwiger’s conjecture for graphs with forbidden holes (with undergraduate student Brian Thomas),  SIAM J.  Discrete Mathematics 31 (2017) 1572-1580.
• Double-critical graph conjecture for claw-free graphs (with PhD student Martin Rolek),  Discrete Mathematics 340 (2017) 1633-1638.
• Intrinsic Evolution of Truncated Puiseux Series on a Mixed-Signal Field Programmable SoC (with Vignesh Thangavel and Ronald DeMara), IEEE Access 4 (2016) 2863-2872.
• A note on weighted rooted trees (with PhD students Talon Ward and Alex York),     Discrete Mathematics 338 (2015) 2492-2494.
• On the size of graphs of class 2 whose core has maximum degree two (with K. M. Koh), Graphs and Combinatorics 29 (2013) 1429-1441.
• Hadwiger number and chromatic number for near regular degree sequences (with N. Robertson), J. Graph Theory 64 (2010) 175-183.
• Independence number and clique minors (with Ken-ichi Kawarabayashi), J. Graph Theory 56 (2007) 219-226.
• Some remarks on the odd Hadwiger’s conjecture  (with Ken-ichi Kawarabayashi), Combinatorica 27 (2007) 429-438.
• The extremal function for K_9 minors (with Robin Thomas), J. Combinatorial Theory, Ser. B 96 (2006) 240-252.
• The extremal function for K_8- minors, J. Combinatorial Theory,  Ser. B 95 (2005) 300 -317.
• The chromatic index critical graphs of even order with five major vertices (with H. P. Yap), Graphs and Combinatorics 21 (2005) 239-246.
• A further extension of Yap’s construction for \Delta-critical graphs,  Discrete Mathematics 243 (2002), 283-290.
• Chromatic index critical graphs of odd order with five major vertices, J. Combin. Math. Combin. Comput. 41 (2002) 161-186.
• Alternative proofs of three theorems of Chetwynd and Hilton (with H. P. Yap), J. Combin. Math. Combin. Comput. 36 (2001) 237-246.
• An extremal problem on the potentially P_k-graphic sequences (with J-S. Li), Discrete Mathematics 212 (2000) 223-231.
• On the potentially P_k-graphic sequences (with Jiong-Sheng Li), Discrete Mathematics 195 (1999) 255-262.
• The smallest degree sum that yields potentially P_k-graphic sequences (with J-S. Li), J. Graph Theory 29 (1998) 63-72.
• The Erdös-Jacobson-Lehel conjecture on potentially P_k-graphic sequences is true (with J-S. Li and R. Luo), Science in China, Ser. A 41 (1998) 510-520.
• The Erdös-Jacobson-Lehel conjecture about potentially P_k-graphic sequences (in Chinese) (with J-S. Li and P. Wang), J. China Univ. Sci. Tech.