报告题目：On the fractional coloring of planar graphs without intersecting triangles and triangular 5-cycles

报告人：胡小兰 副研究员

报告时间：2026年1月10日10:00-11:00

报告地点：科技园阳光楼南815

邀请人：林启忠

邀请单位：福州大学数学与统计学院

报告内容简介：For positive integers $s$ and $t$ with $s\ge t$, a fractional {\em $(s:t)$-coloring} $\phi$ of a graph $G$ is a set coloring that assigns a $t$-element subset of $\{1,\ldots, s\}$ to each vertex such that $\phi(u)\cap \phi(v)=\emptyset$ for each edge $uv\in E(G)$. Two triangles are intersecting if they have at least one vertex in common and a cycle $C$ is triangular if $C$ has at least one edge in common with a triangle. Borodin and Raspaud [{\em J. Combin. Theory Ser. B}, 88(2003) 17-27] conjectured that every planar graph without intersecting triangles or 5-cycles is 3-colorable. In this talk, we show that every planar graph without intersecting triangles and triangular 5-cycles is $(7:2)$-colorable.

报告人简介：胡小兰，副研究员，博士生导师。研究方向为图论及其应用，在Adv. Comb.，J. Graph Theory，SIAM J. Discrete Math., European J. Combin.等专业领域权威期刊发表学术论文三十多篇。先后访问了美国西弗吉尼亚大学、捷克查理大学、德国亚琛工业大学，现为美国数学会《数学评论》(Mathematical Reviews)评论员。主持国家自然科学基金面上项目2项、青年项目1项，湖北省自然科学基金1项。