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)
Line graph of a hypergraph graph.). In hypergraph theory, it is often natural to require that hypergraphs be "k"-uniform. Every graph is the line graph of some hypergraph, but, given a fixed edge size "k", not every graph is a line graph of some "k"-uniform hypergraph. A main problem is to characterize those that are, for each "k" ≥ 3. A hypergraph is linear if each pair of hyperedges intersects in at most one vertex. Every graph is the line graph, not only of some hypergraph, but of some linear hypergraph . characterized line graphs of graphs by a list of 9 forbidden induced subgraphs.