  Cobweb posets uniquely represented by directed acyclic graphs are such a
generalization of the Fibonacci tree that allows joint combinatorial
interpretation for all of them under admissibility condition. This
interpretation was derived in the source papers ([6,7] and references therein
to the first author).[7,6,8] include natural enquires to be reported on here.
The purpose of this presentation is to report on the progress in solving
computational problems which are quite easily formulated for the new class of
directed acyclic graphs interpreted as Hasse diagrams. The problems posed there
and not yet all solved completely are of crucial importance for the vast class
of new partially ordered sets with joint combinatorial interpretation. These so
called cobweb posets - are relatives of Fibonacci tree and are labeled by
specific number sequences - natural numbers sequence and Fibonacci sequence
included. The cobweb posets might be identified with a chain of di-bicliques
i.e. by definition - a chain of complete bipartite one direction digraphs [6].
Any chain of relations is therefore obtainable from the cobweb poset chain of
complete relations via deleting arcs in di-bicliques of the complete relations
chain. In particular we response to one of those problems [1].

Combinatorics;Discrete Mathematics