Chicken (game) respectively. The line in graph on the left shows the optimum probability of playing the escalated strategy for player Y as a function of "x". The line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of "y" (the axes have not been rotated, so the dependent variable is plotted on the abscissa, and the independent variable is plotted on the ordinate). The Nash equilibria are where the players' correspondences agree, i.e., cross. These are shown with points in the right hand graph. The best response mappings agree (i.e., cross)
Extremal graph theory was 1975 when Szemerédi proved his result a vital tool in attacking extremal problems. A typical result in extremal graph theory is Turán's theorem. It answers the following question. What is the maximum possible number of edges in an undirected graph "G" with "n" vertices which does not contain "K" (three vertices "A", "B", "C" with edges "AB", "AC", "BC"; i.e. a triangle) as a subgraph? The complete bipartite graph where the partite sets differ in their size by at most 1, is the only extremal graph with this property. It contains edges. Similar questions have been studied with various