On two cycles of consecutive even lengths
主 讲 人 ：李斌龙 教授
地 点 ：理科群1号楼D-204
Bondy and Vince showed that every graph with minimum degree at least three contains two cycles of lengths diﬀering by one or two. We prove the following average degree counterpart that every n-vertex graph G with at least 5(n−1)/2 edges, unless 4|(n−1) and every block of G is a clique K5, contains two cycles of consecutive even lengths. Our proof is mainly based on structural analysis, and a crucial step which may be of independent interest shows that the same conclusion holds for every 3-connected graph with at least 6 vertices. This solves a special case of a conjecture of Verstraëte. The quantitative bound is tight and also provides the optimal extremal number for cycles of length two modulo four. Joint work with Jun Gao, Jie Ma, Tianying Xie.
李斌龙，西北工业大学教授，博士生导师。荷兰Twente大学博士，捷克West Bohemia大学博士后，丹麦技术大学访问学者。主要研究方向为图的Hamilton性及图的Ramsey理论。主持国家自然科学基金青年项目、面上项目各一项。在 JCTB, J. Graph Theory, European J. Combinatorics等期刊发表论文60余篇。