We determine the number of perfect matchings and forests in a family Tr;3 of triangulated prism graphs. These results show that the extremal number of perfect matchings in a planar graph with n vertices is bounded below by 6 p 7 + p 37 n = (1:535 n ) and the extremal number of forests contained in a planar graph with n vertices is bounded below by 3 p 138:74876 n = (5:1769 n ). The current best
['Michael Biro']
Planar Graphs with Many Perfect Matchings and Forests