报告题目1：Planar graphs are acyclically edge (∆ + 5)-colorable

报告人：舒巧君副教授，杭州电子科技大学

报告时间：2026年9月29日（周二）18:30-19:30

报告地点：腾讯会议：255695667

报告摘要：An acyclic edge coloring of a graph G is a proper edge coloring suchthat no bichromatic cycles are produced. The acyclic chromatic index a′(G) of Gis the smallest integer k such that G has an acyclic edge coloring using k colors.The acyclic edge coloring conjecture by Fiamčik (1978) and Alon, Sudakov and Zaks(2001) states that every simple graph with maximum degree ∆ is acyclically edge(∆ + 2)-colorable. Despite many milestones, the conjecture is still unknown true ornot even for planar graphs. In this talk, we first give a survey on the acyclic edgecoloring. Next, we show that every non-trivial planar graph contains a local structure in one of the eight characterized groups;then deal with each local structure to color the edges in the graph acyclically using no more than ∆ + 5 colors by an induction on the number of edges.

报告人简介：舒巧君，杭州电子科技大学副教授。主要研究图的染色及标号等相关问题，主持完成国家自然科学基金青年基金项目《图的无圈边色数及相关参数的研究》和浙江省自然科学青年基金项目《图的无圈边染色和(2,1)-全标号问题》，参与省级及以上项目若干项。相关研究成果发表在《Joumnal of Graph Theory》、《European Journal of  Combinatorics》、《Journal of Combinatorial Optimization》、《Discrete Applied Mathematics》、《Discrete Mathematics》、《中国科学A辑》等国内外知名期刊上。曾先后访问中国香港浸会大学和加拿大阿尔伯塔大学。

报告题目2：Degree-balanced decompositions into three forests

报告人：宋宁博士，山东理工大学

报告时间：2026年9月29日（周二）19:30-20:30

报告地点：腾讯会议：255695667

报告摘要：For a nonnegative real numberq and a positive integer k, a k-forest decomposition
is q-balanced if  for every  and . For k≥2, an ordered k-forest decomposition is q-quasi-balanced if  for every  and . If the inequalities are required only on , the decomposition is q-balanced onS or q-quasi-balanced on S, respectively.

We prove three structural decomposition results for graphs of arboricity at most three. Every such graph has an11/3-balanced3-forest decomposition. Ifh is the number of vertices whose degrees are not divisible by three, the decomposition can be chosen to be10/3-balanced outside at most
vertices. We also prove that every graph of arboricity at most three has a 2-quasi-balanced3-forest decomposition
in which F is a spanning tree in every component.

These structural results yield maximum-degree consequences. Every graph G of arboricity at most three has a decomposition into three forests whose maximum degrees are at most
. In particular, all three forests can be chosen with maximum degree at most eight when
, at most
when
, and at most  when
. If
and each component contains at most five13-vertices, all three forests can be chosen with maximum degree at most seven. The quasi-balanced decomposition gives the bound
with no lower bound on
. Since every simple planar graph has arboricity at most three, all these maximum-degree conclusions apply in particular to simple planar graphs.

报告人简介：宋宁，山东理工大学数学与统计学院数学系教师，主要研究方向为图论及其应用。2016年于南开大学获理学博士学位，在浙江师范大学数学系从事博士后工作，并顺利出站。参与省级及以上项目若干项。相关研究成果发表在《Journal of Combinatorial Theory, Series B》、《Discrete Applied Mathematics》、《Discrete Mathematics》、《MATCH Communications in Mathematical and in Computer Chemistry》等国内外知名期刊上。

邀请人：数学研究所