Foraging graphs: Constraint rules on matching between bees and flowers in a two-sided pollination market

We present a theorem on foraging graphs which yields bounds on the number of generalists and specialists in a two-sided natural market. With the biological assumption of the Ideal Free Distribution for each forager which visits different flower types, we use our previous game theory approach of matching between bees and flowers (Peleg & Shmida, 1992, Games and Economic Behav., 4, 232-251.) and some concepts of graph theory, to determine the minimum number of specialist foragers and the maximum number of generalists in a two-sided pollination market with homogeneous good. Our theory applies also when the different types of nectar (goods) are not homogeneous but are still substitutional.