Combinatoral problems on matching extension and graph factors

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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.