[1] 国家自然科学基金资助项目：图的结构理论及其算法, 2004.1---2005.12.
[2] 国家自然科学基金资助项目：图因子、路系统及相关问题, 2007.1---2009.12.
[3] 2006年湖北省科技三项费（省攻关计划）：网络信息处理的容错性研究, 2006.12---2009.12.
[4] 2007年湖北省教育厅高等学校省级教学研究项目：高等数学分层教学模式中创新能力培养的研究与实践.
[5] 国家自然科学基金资助项目：图中结构与全局参数, 2011.1---2013.12.
[6] 湖北省高等学校优秀中青年科技创新团队计划项目: 可靠和稳定的网络模型与控制, 2011.1-2014.12.
[7] 国家自然科学基金资助项目：群连通度和子图存在性及相关问题的研究, 2012.1—2015.12.
[8] 国家自然科学基金资助项目：图中参数与子图存在性问题研究, 2014.1---2017.12.
[9] 国家自然科学基金资助项目：图中包含特定元素的子图结构研究, 2018.1---2021.12.

          
        

[1] Hongmei Liu and Yingying Liu, The Hamilton Path in Faulty Enhanced, Lecture Notes in Electrical Engineering Vol.126, 2012-4, pp 867-872. (EI)
[2] Qing Liu, Hongmei Liu, yanjuan Zhang,Yihan Fan, Routing Algorithm in FQn with a Large Number of Faulty Nodes, The 2th International Conference on Consumer electronics, communication and networks, 2012-4, Three Gorges,1286-1289. (EI)
[3] Min Liu, Hongmei Liu, Cycles in Conditional faulty Enhanced Hypercube Networks, Journal of Communications and Networks（ISSN：1229-2370）, Vol. 14, No. 2, 2012-4,  213-221.(SCI)
[4]  Min Liu, Hongmei Liu, Paths and cycles embedding on faulty enhanced hypercube networks, Acta Mathematica Scientia, 2013, 33B(1),pp.227-246. (SCI)
[5] Xiaojuan He, Hongmei Liu, Qing Liu;  Cycle Embedding in Faulty Folded Hypercube, International Journal of Applied Mathematics and Statistics, Vol.37, No.7, 2013，pp.97—109, ISBN:978-0-7695-47895-3. ISSN 0973-1377(print), ISSN 0973-7545(online)（EI）
[6] Shilong Cao, Hongmei Liu, Xiaojuan He, On constraint Fault-free Cycles in Folded Hypercube, International Journal of Applied Mathematics and Statistics, Vol.42, No.12, 2013，pp.38—44, ISBN:978-0-7695-47895-3. ISSN 0973-1377(print), ISSN 0973-7545(online) （EI）
[7] Xiaojuan He, Hongmei Liu, node-to-node disjoint paths in hypercube networks with faulty edges, Proceedings 2013 IEt international conference on information and communications technologies, April 27-29th, 2013, 336-339 (EI)
[8]  Qing Liu, Hongmei Liu, Runlan Qin, Extended Local-connectivity on Folded Hypercube with a Large Number of Faulty Nodes,  International Journal of Applied Mathematics and Statistics, Vol.50, No.20, 2013，pp.102—108, ISSN 0973-1377(print), ISSN 0973-7545 （EI）
[9]  Qing Liu, Hongmei Liu, Runlan Qin, Paths in Enhanced Hypercube with a Large Number of Faulty Nodes,  International Journal of Applied Mathematics and Statistics, Vol.51, No.21, 2013，pp.44—51, ISSN 0973-1377(print), ISSN 0973-7545(online) （EI）
[10] Yanjuan Zhang, Hongmei Liu, Min Liu, VERTEX-FAULT CYCLES EMBEDDING ON ENHANCED HYPERCUBE NETWORKS, Acta Mathematica Scienta, 2013, 33B(6):1579—1588  (SCI)
[11] Runlan Qin, Hongmei Liu, A Further Result on Cycles in Conditional Faulty Enhanced Hypercubes, International Journal of Applied Mathematics and Statistics, Vol.52, No.2, 2014，pp.49—54, ISSN 0973-1377(print), ISSN 0973-7545 （EI）
[12] Yihan Fan, Hongmei Liu, Juan Mei, Semiglobal Finite-Time Synchronization of Complex Dynamical Networks via Periodically Intermittent Control, Abstract and Applied Analysis, Vol.(2015) 2015(SCI)
[13 ] Min Liu, Hongmei Liu, Vertex-Fault-Tolerant Cycle Embedding on Enhanced Hypercube Networks, Acta Mathematicae Applicatae Sinica, English Series, Vol.32, No.1, 2016: 187—198 (DOI:10.1007/s10255-016-0547-z, (SCI)
[14] Liu Hongmei, Tang Maozeng, Fault-tolerant cycles embedding in Folded hypercube, Wuhan University Journal of National Sciences, Vol.21, No.3, 2016, 191—198. (ISSN: 1007-1202, DOI 10.1007/s11859-016-1158-5) 
[15] Hongmei Liu, Maozeng Tang and Dan Yuan, "Some New Results on Fault-tolerant Cycles Embedding in Folded Hypercubes", Journal of Combinatorial Mathematics and Combinatorial Computing , pp. 23-36, Vol.97 , May, 2016
[16] Hongmei Liu, Dan Jin, An algorithm on disjoint paths in enhanced hypercubes, Journal of Combinatorial Mathematics and Combinatorial Computing , pp.267-280, Vol.103 , November, 2017.(EI )
[17]  Dan JIN and Hong-mei LIU, The Structure Fault-Tolerance of Enhanced Hypercube Networks, 2018 International Conference on Electrical, Control, Automation and Robotics, 235—238. (SCIE)
[18] Yanjuan Zhang, Hongmei Liu, Dan Jin, The Edge-hamiltonicity of Exchanged Folded
Hypercubes, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol.107 , November, 2018: 127-136
[19] Hongmei Liu, Dan Jin, The Maximum Number of Disjoint Paths in Faulty Enhanced Hypercubes, Journal of Combinatorial Mathematics and Combinatorial Computing , pp. 99-112, Vol.108 , February, 2019.(EI )
[20] Yanjuan Zhang and Hongmei Liu, "The Structure connectivity of Enhanced Hypercube Networks", Journal of Combinatorial Mathematics and Combinatorial Computing ,pp. 171-180, Vol.110 , August, 2019(EI )
[21] Hongmei Liu, Dan Jin, The Maximum Number of Disjoint Paths in Faulty Enhanced Hypercubes, Journal of Combinatorial Mathematics and Combinatorial Computing , pp. 99-112, Vol.108 , February, 2019.
[22] Yihan Fan, Jun Mei, Hongmei Liu*,Yuling Fan, Fuxiang Liu, Fast Synchrozation of complex networks via Aperiodically intermittent sliding mode control, Neural processing Letters （2020）(SCI )

刘红美老师曾获三峡大学第一届“学生评教免评教师”称号；荣获三峡大学第四届“师德标兵”、三峡大学“三八红旗手”称号，2007年被评为湖北省教育工会先进女职工。2009年 湖北省高等学校教学成果三等奖，教学研究成果三等奖（《数学分析》课程教学改革研究与实践）。2016年留学生“线性代数”获湖北省品牌课程。

[1] 刘红美 陈虎叶 《图论应用基础》（英文版），华中师范大学出版社，2020.10. 
[2] 刘红美《离散数学》（英文版），华中师范大学出版社，2022.8.