Sandwich problem for Π- and Δ-free multigraphs and its applications to positional games

As a motivation and application, we consider the n-person positional game forms, which are known to be in a one-to-one correspondence with the Π- and Δ-free n-graphs. Given a game form g, making use of the above result, we recognize in polynomial time whether g is a subform of a positional (that is, tight and rectangular) game form and, if yes, we generate with polynomial delay all such positional extensions of g.