Topological properties of Landau curves in connection with Mandelstam's conjecture

Feynman amplitude $F_G$ assotiated with the Feynman graph $G$ is considered for the case of the scalar scattering reaction of the $1+2\to 3+4$ type. Sufficient conditions of validity of the Mandelstam hypothesis [1] are found as conditions on the Landau curves $\mathscr L_G$ for the amplitude $F_G$, $G\in \Re$ where $\Re$ is a certain class of the Feynmann graphs introduced in the work. Application of the criteria obtained to the ladder graph is considered.