符号图在曲面上的准亏格与最大准亏格

项目名称： 符号图在曲面上的准亏格与最大准亏格

项目编号： No.11301171

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 吕胜祥

作者单位： 湖南科技大学

项目金额： 22万元

中文摘要： 符号图在曲面上的定向嵌入是拓扑图论的最新研究方向之一。基于Zaslavsky、Siran、Archdeacon等提出的系列科学问题与猜想，本项目将对符号图定向嵌入到曲面上的准亏格与最大准亏格展开研究，主要内容包括：研究符号图并图的准亏格可加性；计算完全图、完全二部图等典型图类的具体符号图的准亏格；确定完全图、完全二部图等典型图类的所有符号图准亏格的最大值或上界；给出符号图的最大准亏格下界；刻画符号图的可单面定向嵌入性；探索符号图的Betti-亏数稳定性；设计符号图最大准亏格定向嵌入有效算法；建立符号图可定向嵌入曲面插值定理。

中文关键词： 准亏格；最大准亏格；定向嵌入；符号图；亏格

英文摘要： The orientation embedding of signed graphs on surfaces is a latest research direction of topological graph theory. Following a series of problems and conjectures putted forward by Zaslavsky,Siran and Archdeacon,etc., the demigenus and maximum demigenus of signed graphs on surfaces is investigated in this project. The research contents of this project mainly involves: studying the demigenus additivity of the union of signed graphs; calculating the demigenus of some signed graphs of complete graphs and complete bipartite graphs,etc.; determining the largest demigenus or upper bound over all singed graphs of complete graphs and complete bipartite graphs,etc.; obtaining the lower bound on maximum demigenus of signed graphs; characterizing the single face orientation embeddability of signed graphs; describing the Betti-deficiency stability of signed graphs; constructing effective algorithms for maximum demigenus orientation embedding; establishing an interpolation theorem for the surfaces on which the signed graphs can be orientation embedded.

英文关键词： Demigenus；Maximum Demigenus；Orientation embedding；Signed graphs；Genus