The Application Of Graph Theory In Mathematical Competition

In High School Mathematics Competition, m×n rectangle of the graphics overlap problem has been one of the most prevailing questions.With the continuous development of mathematics and the computer applications in mathematics and the deepening of the content of mathematics competition.The graphics overlap problem have been brought to our attention.In this paper, according to the covering questions in recent year competitions,we will research in details the m×n rectangle of the graphics overlap problem.The whole article can be divided into several parts:a.Introduce the concept of complete covering, saturated covering,covering with the same figure and covering with the different figures.Define "the basic figure".Such as the figure of k-L、4-Z、4-T and1×2domino.b.Discusse seven basic methods of covering.c.Research four different kinds of m×n rectangle covering questions:complete covering with the same figure, complete covering with the different figures, saturated covering with the same figure, saturated covering with the different figures.d. Six propositions are given on the four kinds of m×n rectangle covering.In this paper, we will use the literature analysis, according to the content of mathematic competition, m×n rectangle covering, a kind of typical question, is studied which is also beneficial for connecting the research of mathematic competition with middle school teaching.