講座主題：1-平面圖中的匹配 Matchings in 1-planar graphs
專(zhuān)家姓名：黃元秋
工作單位：湖南師范大學(xué)
講座時(shí)間：2023年12月07日 9:30-11:30
講座地點(diǎn)：騰訊會(huì)議：117 478 382
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recently, Biedl and Wittnebel proved that every 1-planar graph with minimum degree 3 and n≥7 vertices has a matching of size at least (n+12)/7, and this is tight for some graphs; they also provided tight lower bounds on the matching of sizes for 1-planar graphs with minimum degree 4 and 5. In this paper, we show that any 1-planar graph with minimum degree 6 and n≥32 vertices has a matching of size at least (3n+4)/7, and this lower bound is tight. Our result confirms a conjecture posed by Biedl and Wittnebel.
主講人介紹：
黃元秋，湖南師范大學(xué)二級(jí)教授、博士、博士生導(dǎo)師，教育部“新世紀(jì)優(yōu)秀人才”入選者，湖南省普通高校學(xué)科帶頭人?，F(xiàn)為湖南師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院副院長(zhǎng)、中國(guó)組合數(shù)學(xué)與圖論學(xué)會(huì)理事、中國(guó)運(yùn)籌學(xué)會(huì)理事、湖南省數(shù)學(xué)學(xué)會(huì)常務(wù)理事。1996年博士畢業(yè)于中國(guó)科學(xué)院應(yīng)用數(shù)學(xué)研究所, 主要從事圖論與組合中相關(guān)問(wèn)題的研究，包括圖的虧格及最大虧格、圖在曲面上的嵌入分布、圖的交叉數(shù)、圖的k-平面性等。在 J. Combin. Theory Ser. B、J. of Graph Theory、 SIAM J. Discrete Math., Discrete Math.、 Discrete Applied Math.、Euro. Combin.、The Electronic Journal of Combinatorics、Graphs and Combinatorics以及 《中國(guó)科學(xué)》等國(guó)內(nèi)外學(xué)術(shù)期刊上發(fā)表論文120余篇。6次主持國(guó)家自然科學(xué)基金項(xiàng)目 及省部級(jí)科研項(xiàng)目多次。
