Xiaofeng Gu

I'm a Professor of Mathematics in the Dr. James 'Earl' Perry College of Mathematics, Computing, and Sciences at University of West Georgia. I joined UWG as an Assistant Professor in August 2015; and obtained my PhD in Mathematics from West Virginia University in 2013 under the supervision of Hong-Jian Lai. Here is my profile at UWG and my Google Scholar. My Erdős number is 2 (via Guantao Chen or Ron Gould).

Research interests

Combinatorics, graph theory and applications. Currently I'm particularly interested in

Interplay between graph theory and linear algebra
Packing spanning trees and other spanning structures
Connectivity of graphs and hypergraphs

External grant

Collaboration Grants for Mathematicians (now called Travel Support for Mathematicians), Simons Foundation (2017--2022, extended to 2024).

Editorial board

Associate editor of Discrete Mathematics, Algorithms and Applications (DMAA), 09/2022--present.

Publications

Dissertation

[D1] Connectivity and spanning trees of graphs, PhD Dissertation, West Virginia University, 2013.

Conference Proceedings

[C2] Cyclically orderable generalized Petersen graphs (with William Zhang), Proceedings of the 16th International Conference on Algorithmic Aspects in Information and Management (AAIM 2022), Lecture Notes in Computer Science 13513 (2022), 303-315. (The journal version is [J39].)

[C1] Improved algorithm for detecting negative cost cycles in undirected graphs (with K. Madduri, K. Subramani and H.-J. Lai), Proceedings of the Third Annual International Frontiers of Algorithmics Workshop (FAW), Lecture Notes in Computer Science 5598 (2009) 40-50.

Journal papers

[J43] Cyclic base ordering of certain degenerate graphs (with Jessica Li, Eric Yang and William Zhang), Discrete Applied Mathematics 362 (2025), 148-156.

[J42] l‐connectivity, l‐edge‐connectivity and spectral radius of graphs (with Dandan Fan and Huiqiu Lin), Journal of Algebraic Combinatorics 60 (2024), 929-947. (arXiv:2309.05247)

[J41] A unified combinatorial view beyond some spectral properties (with Muhuo Liu), Journal of Algebraic Combinatorics 60 (2024), 817-841. (arXiv:2205.15228)

[J40] Spectral characterization of the complete graph removing a cycle (with Muhuo Liu, Haiying Shan and Zoran Stanić), Journal of Combinatorial Theory, Series A 205 (2024), 105868.

[J39] Cyclic base ordering of generalized Petersen graphs (with William Zhang), Discrete Mathematics, Algorithms and Applications 16(2) (2024), 2350019. (This is the journal version of [C2].)

[J38] Spectral radius and edge-disjoint spanning trees (with Dandan Fan and Huiqiu Lin), Journal of Graph Theory 104 (2023) no. 4, 697-711. (arXiv:2207.04701, JGT Top Cited Article in 2023)

[J37] Graph rigidity properties of Ramanujan graphs (with Sebastian M. Cioabă, Sean Dewar and Georg Grasegger), The Electronic Journal of Combinatorics 30(3) (2023), #P3.12. (arXiv:2206.03983)

[J36] Spanning tree packing and 2-essential edge-connectivity (with Runrun Liu and Gexin Yu), Discrete Mathematics 346 (2023), 113132. (arXiv:2208.12922)

[J35] l-Connectivity and l-edge-connectivity of random graphs (with Ran Gu, Yongtang Shi and Hua Wang), Journal of Graph Theory 101 (2022) no. 1, 5-28.

[J34] On hamiltonian line graphs of hypergraphs (with Hong-Jian Lai and Sulin Song), Journal of Graph Theory 100 (2022) no. 3, 489-503.

[J33] Graph toughness from Laplacian eigenvalues (with Willem H. Haemers), Algebraic Combinatorics, Volume 5 (2022) no. 1, 53-61. (arXiv:2104.03845)

[J32] Extremal augmented Zagreb index of trees with given numbers of vertices and leaves (with Chaohui Chen, Muhuo Liu, and Kinkar Chandra Das), Discrete Mathematics 345-4 (2022), 112753.

[J31] Spectral strengthening of a theorem on transversal critical graphs (with Muhuo Liu), Discrete Mathematics 345-3 (2022), 112717. (arXiv:2008.07474)

[J30] A tight lower bound on matching number of graphs via Laplacian eigenvalues (with Muhuo Liu), European Journal of Combinatorics 101 (2022), 103468. (arXiv:2103.11550)

[J29] Sufficient conditions for 2-dimensional global rigidity (with Wei Meng, Martin Rolek, Yue Wang and Gexin Yu), SIAM Journal on Discrete Mathematics 35-4 (2021), 2520-2534. (arXiv:2106.08539)

[J28] Spectral conditions for graph rigidity in the Euclidean plane (with Sebastian M. Cioabă and Sean Dewar), Discrete Mathematics 344 (2021), 112527. (arXiv:2001.06934)

[J27] A proof of Brouwer's toughness conjecture, SIAM Journal on Discrete Mathematics 35-2 (2021), 948-952. (arXiv:2010.05065, SCMS talk)

[J26] Spectral characterization of the complete graph removing a path: Completing the proof of Camara-Haemers Conjecture (with Muhuo Liu), Discrete Mathematics 334 (2021), 112275.

[J25] Toughness in pseudo-random graphs, European Journal of Combinatorics 92 (2021), 103255.

[J24] Spectral characterization of the complete graph removing a path (with Muhuo Liu and Haiying Shan), Discrete Applied Mathematics 284 (2020), 499-512.

[J23] Spanning bipartite graphs with high degree sum in graphs (with Guantao Chen, Shuya Chiba, Ronald J. Gould, Akira Saito, Masao Tsugaki and Tomoki Yamashita), Discrete Mathematics 343 (2020), 111663.

[J22] Unified extremal results for vertex-degree-based graph invariants with given diameter (with Muhuo Liu and Yuedan Yao), MATCH Communications in Mathematical and in Computer Chemistry 82 (2019), 699-714.

[J21] Spanning rigid subgraph packing and sparse subgraph covering, SIAM Journal on Discrete Mathematics 32 (2018), 1305-1313. (arXiv:1405.0247)

[J20] Cycles with a chord in dense graphs (with Guantao Chen, Ronald J. Gould and Akira Saito), Discrete Mathematics 341 (2018), 2131-2141.

[J19] A property on reinforcing edge-disjoint spanning hypertrees in uniform hypergraphs (with H.-J. Lai), Discrete Mathematics 341 (2018), 400-404.

[J18] Spectrum bounds for the scattering number, integrity, tenacity of regular graphs (with Yinkui Li and Yongtang Shi), Future Generation Computer Systems 83 (2018), 450-453.

[J17] Packing spanning trees and spanning 2-connected k-edge-connected essentially (2k-1)-edge-connected subgraphs, Journal of Combinatorial Optimization 33 (2017), 924-933.

[J16] Connectivity, toughness, spanning trees of bounded degrees, and spectrum of regular graphs(with S.M. Cioabă), Czechoslovak Mathematical Journal (special issue dedicated to Professor Miroslav Fiedler) 66 (2016), 913-924. (arXiv:1602.05922)

[J15] Fractional spanning tree packing, forest covering and eigenvalues (with Y. Hong, H.-J. Lai and Q. Liu), Discrete Applied Mathematics 213 (2016), 219-223.

[J14] Spectral conditions for edge connectivity and packing spanning trees in multigraphs, Linear Algebra and its Applications 493 (2016), 82-90.

[J13] Edge-disjoint spanning trees, edge connectivity and eigenvalues in graphs (with H.-J. Lai, P. Li and S. Yao), Journal of Graph Theory 81 (2016), 16-29.

(JGT Most Cited Top 3 Papers in 2015-2016)

[J12] Augmenting and preserving partition connectivity of a hypergraph (with H.-J. Lai), Journal of Combinatorics 5 (2014), 271-289.

[J11] Regular factors and eigenvalues of regular graphs, European Journal of Combinatorics 42 (2014) 15-25.

[J10] Note on edge-disjoint spanning trees and eigenvalues (with Q. Liu, Y. Hong and H.-J. Lai), Linear Algebra and its Applications 458 (2014) 128-133.

[J9] Characterizations of strength extremal graphs (with H.-J. Lai, P. Li and S. Yao), Graphs and Combinatorics 30 (2014) 1453-1461.

(Previous title: Characterizations of minimal graphs with equal edge connectivity and spanning tree packing number)

[J8] Cyclic base orderings in some classes of graphs (with K. Horacek and H.-J. Lai), Journal of Combinatorial Mathematics and Combinatorial Computing 88 (2014) 39-50.

[J7] Realizing degree sequences with $k$-edge-connected uniform hypergraphs (with H.-J. Lai), Discrete Mathematics 313 (2013) 1394-1400.

[J6] Improved algorithms for optimal length resolution refutation in difference constraint systems (with K. Subramani and M. Williamson), Formal Aspects of Computing 25 (2013) 319-341.

[J5] Multigraphic degree sequences and supereulerian graphs, disjoint spanning trees (with H.-J. Lai and Y. Liang), Applied Mathematics Letters 25 (2012) 1426-1429.

[J4] Characterization of minimally $(2,l)$-connected graphs (with H.-J. Lai and S. Yao), Information Processing Letters 111 (2011) 1124-1129.

[J3] Absorbing random walks and the NAE2SAT problem (with K. Subramani), International Journal of Computer Mathematics 88 (2011) 452-467.

[J2] Group connectivity in products of graphs (with J. Yan, S. Yao and H.-J. Lai), International Journal of Algebra 4 (2010) 1185-1200.

[J1] Random walks for selected Boolean implication and equivalence problems (with K. Subramani and H.-J. Lai), Acta Informatica 46 (2009) 155-168.

Conferences and talks

Here is a list of upcoming Combinatorial Conferences maintained by Douglas B. West.
Following David Galvin and Sebi Cioaba, this is a map of the US states where I have given a talk. Consider inviting me to your state😊

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