On the evening of June 18, 2026, at the invitation of the School of Mathematics of our university, three distinguished scholars delivered consecutive online academic lectures via Tencent Meeting (Meeting ID: 895 980 255). The speakers were Professor Guanghui Wang and Professor Bingqiang Liu from the School of Mathematics, Shandong University, and Professor Bo Ning from the School of Cryptography and Cyberspace Security & School of Computer Science, Nankai University. Covering the historical lineage of classical graph theory problems, frontier theoretical breakthroughs and interdisciplinary applications, the series drew wide participation from faculty members and students across the university both online and offline, fostering a rich academic atmosphere.

The first lecture, entitled Several Classical Problems in Graph Theory, was delivered by Professor Guanghui Wang. As a core branch of discrete mathematics, graph theory underpins a broad spectrum of fields including combinatorial optimization, algorithm design and theoretical computer science. Among its numerous research directions, graph coloring theory and Ramsey theory stand as two long-standing, highly influential strands with profound theoretical significance and practical value. Focusing on these two classical themes, Professor Wang traced the historical evolution of core problems in the field systematically, starting from the origins of foundational conjectures and landmark theorems. He walked the audience through the iteration of key research paradigms over decades, and presented the latest research outcomes achieved by his team in both directions.

Weaving classical problem backgrounds together with cutting-edge progress, Professor Wang elucidated not only the intrinsic mathematical logic behind core conclusions, but also the applied value of relevant theories in interdisciplinary scenarios. At the end of his talk, he shared his insights into future trends in graph theory research, and outlined multiple promising directions for early-career scholars to explore in depth. In the Q&A session, participating faculty and students actively raised questions on the derivation details of key theorems, technical pathways of frontier research, and entry points for newcomers to the field. Professor Wang responded to each query with thorough and in-depth explanations, providing targeted guidance for the audience’s academic doubts.

The second session featured Professor Bingqiang Liu’s report entitled A Brief Discussion on Bioinformatics and Mathematics. Focusing on the interdisciplinary integration of mathematics and biomedicine, the report drew broad attention from teachers and students with backgrounds in mathematics, biology and related disciplines.

Mathematical problems permeate every stage of bioinformatics data processing and mining. With the explosive growth of biomedical data in recent years, applying mathematical methods to extract core biological insights from massive, complex datasets has emerged as a pivotal challenge at the intersection of the two fields. Starting from two core research scenarios — genome assembly and gene regulatory network analysis — Professor Liu systematically illustrated the application paradigms of graph theory and complex network methods in bioinformatics. He demonstrated how biological sequence assembly problems can be abstracted into graph construction and path-solving problems, and how complex network theory can be applied to model and analyze gene regulatory relationships.

Alongside introducing specific technical methods, Professor Liu offered an in-depth analysis of the opportunities currently facing interdisciplinary mathematics-biomedicine research, as well as the challenges posed by the complexity of biological systems and data noise. He emphasized that the deep integration of mathematical tools with biological domain knowledge is the core driving force for breakthroughs in this field. During the Q&A session, faculty and students raised targeted questions on the technical details of genome assembly, regulatory network modeling methodologies, and career development paths in interdisciplinary research. Professor Liu responded to each question patiently and meticulously, sharing hands-on experience from his long-standing interdisciplinary research work.

The final lecture, entitled Longest Cycles in Strongly Connected Graphs and Dirac-type Results, was given by Professor Bo Ning, focusing on the latest breakthroughs in graph cycle theory. The session was attended by numerous faculty members and graduate students specializing in graph theory and related directions.

The longest cycle problem is one of the core classical topics in graph theory, and has drawn widespread academic attention since the mid-20th century. Foundational results represented by Dirac’s theorem have laid a critical theoretical foundation for research in this field, while a series of classical conjectures have guided the direction of related research for decades. In this lecture, Professor Ning presented the proof of Bondy’s conjecture for all sufficiently large graphs — a long-standing open problem in the field. He explained that a cornerstone of the proof is a newly established Dirac-type theorem, which provides a general lower bound on the length of the longest cycle in k-connected graphs. This result also offers a partial positive answer to a conjecture proposed by Jung in 1990.

Professor Ning further introduced the novel technical tools developed by his research team over the course of the study, including a depth-first search (DFS) lemma and an average-degree analogue of the Bondy-Jackson theorem. To conclude the lecture, he extended the discussion to related open problems in the field, and presented a counterexample to a conjecture put forward by Voss in 1991, revising prior understandings of the relevant problem. After the lecture, attending teachers and students held in-depth exchanges with Professor Ning on the key proof steps for Bondy’s conjecture, generalization approaches for Dirac-type theorems, and the construction method for the Voss conjecture counterexample, with lively and engaging discussions.

This lecture series covered the full landscape of fundamental theoretical frontiers and interdisciplinary applications of graph theory. It enabled attendees to develop a more systematic and profound understanding of the historical lineage and cutting-edge progress of classical graph theory problems, while demonstrating the research thinking and technical methodologies for tackling classical conjectures and solving practical problems in interdisciplinary fields with mathematical tools. The event delivered valuable academic inspiration for teachers and students engaged in related research, and broadened the academic horizons of all participants.