报告名称：On 2-factors with chorded cycles in graphs
主办单位：数学与统计学学院
报告专家：颜谨
专家所在单位：山东大学
报告时间：2019年1月7日
报告地点：数学与统计学学院201报告厅
专家简介：颜谨教授，山东大学博士生导师，任中国运筹学会图论组合分会理事，中国工业与应用数学学会图论组合及其应用专业委员会委员。主要研究方向为图论与网络优化，共发表SCI论文60余篇，主持国家自然科学基金面上项目2项，曾主持省部级基金3项，参与国家基金及省部级基金多项。
报告摘要：For a graph G, a chord of a cycle in a graph G is an edge of G joining two non-consecutive vertices of the cycle. In this paper, we prove the following result, which is an extension of a result of Brandt et al.~(J. Graph Theory 24 (1997) 165--173) for large graphs: For positive integers k and c, there exists an integer f(k, c) such that, if G is a graph of order n≥ f(k, c) and d(u)+d(v) ≥n for any pair of non-adjacent vertices in G, then G has a 2-facotr with exactly k vertex-disjoint cycles, each of which has at least c chords.
报告名称：Edge-face Coloring of Plane Graphs
主办单位：数学与统计学学院
报告专家：王维凡
专家所在单位：浙江师范大学
报告时间：2019年1月7日
报告地点：数学与统计学学院201报告厅
专家简介：王维凡教授，博士生导师，浙江师范大学校学术委员会副主任，基础数学-省重点学科负责人，数学研究所执行所长，中国数学会理事，中国工业与应用数学学会理事，中国组合数学与图论学会理事，浙江省数学会副理事长。主持国家自然科学基金和省自然科学基金项目共6项，在国内外学术刊物上发表论文90余篇,其中被SCI索引60余篇。
报告摘要：The edge-face chromatic numberχef (G) of a plane graph G is the least number of colors such that any two adjacent edges, adjacent faces, and incident edge and face have different colors. In this talk we shall give a survey on the
edge-face coloring and list edge-face coloring of plane graphs. We also show that every 2-connected and simple plane graph G with maximum degree∆≥16 hasχef (G) =∆.
报告名称：图的线性荫度
主办单位：数学与统计学学院
报告专家：吴建良
专家所在单位：山东大学
报告时间：2019年1月7日
报告地点：数学与统计学学院201报告厅
专家简介：吴建良，山东大学教授、博士生导师、系统与运筹研究所所长，中国系统工程学会委员、中国数学会组合数学与图论专业委员会常务委员和副秘书长、中国工业与应用数学学会组合图论及应用专业委员会副主任委员、中国运筹学会图论组合分会常务委员。多次主持国家自然科学基金面上项目并作为主要参与人参加过2项国家自然科学基金重点项目。
报告摘要：本报告主要宣讲图的线性荫度的研究进展，首先介绍图的线性荫度猜想的相关进展，然后推广到图的列表线性荫度、(k,d)-荫度等。
报告名称：A note on transmission feasibility problem in networks
主办单位：数学与统计学学院
报告专家：张运清
专家所在单位：南京大学
报告时间：2019年1月7日
报告地点：数学与统计学学院201报告厅
专家简介：张运清教授，南京大学数学系硕士生导师，主要从事网络优化、Ramsey数等图论与组合优化相关问题的研究。
报告摘要：In the network designing phase, the networkneeds to be built according to certain indicators to ensurethat the network has the ideal functions and can worksmoothly. From a modeling perspective, each site in thenetwork is represented by a vertex, channels between sitesare represented by edges, and thus the entire network canbe denoted as a graph. Problems in the network can betransformed into corresponding graph problems. In particular,the feasibility of data transmission can be transformedinto the existence of fractional factors in networkgraph. This note gives an independent set neighborhoodunion condition for the existence of fractional factors ina special setting, and shows that the neighborhood unioncondition is sharp.
报告名称：On Gallai Ramsey Numbers of Cycles
主办单位：数学与统计学学院
报告专家：陈耀俊
专家所在单位：南京大学
报告时间：2019年1月7日
报告地点：数学与统计学学院201报告厅
专家简介：陈耀俊教授，中国运筹学会理事，南京大学数学系博士生导师，主要从事图中特定子图结构、Ramsey数等图论与组合优化相关问题的研究。近几年主持国家自然科学基金四项，在国内外专业学术杂志上发表多篇研究论文，其中近40篇发表在SCI检索源期刊上。
报告摘要：A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallaik-coloring is a Gallai coloring that useskcolors. Given a graphHand an integerk≥ 1, the Gallai-Ramsey numberGRk(H) ofHis the least positive integerNsuch that every Gallaik-coloring of the complete graphKNcontains a monochromatic copy ofH. LetCndenote a cycle onnvertices. In this talk, we will report our new results on the Gallai-Ramsey numbersGRk(C2n) andGRk(C2n+1).
报告名称：On Minimum (n,k)-Broadcast Graphs
主办单位：数学与统计学学院
报告专家：周国飞
专家所在单位：南京大学
报告时间：2019年1月7日
报告地点：数学与统计学学院201报告厅
专家简介：周国飞教授，南京大学数学系硕士生导师，主要从事图的结构、Ramsey数等图论与组合优化相关问题的研究。
报告摘要：Given a communication network (modelled as a graph), a message is transmitted from an originator to all other vertices in such a way that each message transmission takes one time unit and each vertex participates in at most one transmission to its neighbor per time step. We call this process broadcasting. A broadcast graph with $n$ vertices is an communication network that the broadcasting can be finished from any vertex in optimal time $\lceil \log_2n\rceil$. Among all the broadcast graphs with $n$ vertices, the one which has the minimum number of edges is called a minimum $n$-broadcast graph. In this paper, we generalize the concept of minimum broadcast graph, introduce a new broadcasting model, which is called an $(n,k)$-broadcast graph. The minimum $(n,k)$-broadcast graphs are characterized for $1\le k\le 6$.
