蕴含P-可图序列及其算法研究

研究图论及其应用中当今国际同行关注的几个活跃问题：蕴含极大边连通（超级边连通）可图序列的刻划及其实现的算法、强迫k-边连通（二部）可图序列的最强单调度条件、蕴含m限制边连通可图序列的刻划及其实现的算法、蕴含A-连通二部可图序列的极值问题(其中A是一个（可加的）阿贝尔群且具有单位元0)、蕴含A-连通可图序列的刻划问题及其相关问题、蕴含完全二部图的二部可图序列的两个推广及其实现的算法、蕴含k树可图序列的极值问题及其相关问题等，以推进蕴含P-可图序列及其算法、图的m限制边连通度、A-连通图以及k树的研究和发展，将对图论和理论计算机科学具有重要理论意义和应用前景。

We will investigate the following several active problems in graph theory with applications which are concerned (or interested) by international counterparts at present: the characterization of potentially maximally edge connected (super edge connected) graphic sequence and the algorithm of its realization、the strongest monotone degree condition of forcibly k-edge-connected (bipartite) graphic sequence、the characterization of potentially m-restricted edge connected graphic sequence and the algorithm of its realization、the extremal problem of potentially A-connected bipartite graphic sequence (A is an (additive) abelian group with identity 0)、the characterization of potentially A-connected graphic sequence and its related problem、two extensions of potentially complete bipartite graph bipartite graphic sequence and the algorithm of its realization、the extremal problem of potentially k-tree graphic sequence and its related problem, etc. These results will improve the research and development of potentially P-graphic sequence and its algorithm、m-restricted edge connectivity of graphs、A-connected graphs and k-trees, and also will be important to graph theory and theoretical computer science in theoretical significances and application prospects.