Combinatoral problems on matching extension and graph factors

图论是一个古老的，但重新诞生和充满活力的数学分支。自20世纪60年代以来，由于其在物理学，生物学和运筹学中的广泛应用，特别是计算机和通信网络的广泛使用，它得到了迅速发展。图论作为一种工作框架的引入彻底改变了科学研究的面貌。图论已成为数学中最活跃的分支之一。计算科学也为图论的使用提供了越来越多的机会。 最近，图论也成为研究基因序列和环境可持续性，管理科学和逻辑设计的有用工具。在2006年ICM会议期间，有6个一小时的邀请演讲与组合数学和图论有关，这清楚地证明了数学社会对其重要性的认识。

Graph Theory is an old but re-born and energized branch of mathematics. It has grown rapidly since the 1960's due to its wide range of applications in Physics, Biology and Operations Research, especially since the wide-spread usage of computers and communication networks. The introduction of Graph Theory as a working frame has changed the landscape of scientific investigations completely. Graph Theory has become one of the most active branches of mathematics. Computing science also provides a growing opportunity for the use of Graph Theory. More recently, Graph Theory also became a useful instrument for the study of gene sequences and environment sustainability, management science and logic designing. During the 2006 ICM conference, there were 6 one-hour invited talks related to Combinatorics and Graph Theory, which is clear evidence of the recognition of its importance from the mathematical society.