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For any integer $d$ we introduce a prop $RHra_d$ of oriented ribbonhypergraphs (in which "edges" can connect more than two vertices) and provethat it admits a canonical morphism of props, $$ Holieb_d^\diamond\longrightarrow RHra_d, $$ $Holieb_d^\diamond$ being the (degree shifted)minimal resolution of prop of involutive Lie bialgebras, which is non-trivialon every generator of $Holieb_d^\diamond$. We obtain two applications of thisgeneral construction.  As a first application we show that for any graded vector space $W$ equippedwith a family of cyclically (skew)symmetric higher products the associatedvector space of cyclic words in elements of $W$ has a combinatorial$Holieb_d^\diamond$-structure. As an illustration we construct for each naturalnumber $N\geq 1$ an explicit combinatorial strongly homotopy involutive Liebialgebra structure on the vector space of cyclic words in $N$ graded letterswhich extends the well-known Schedler's necklace Lie bialgebra structure fromthe formality theory of the Goldman-Turaev Lie bialgebra in genus zero.  Second, we introduced new (in general, non-trivial) operations in stringtopology. Given any closed connected and simply connected manifold $M$ ofdimension $\geq 4$. We show that the reduced equivariant homology$\bar{H}_\bullet^{S^1}(LM)$ of the space $LM$ of free loops in $M$ carries acanonical representation of the dg prop $Holieb_{2-n}^\diamond$ on$\bar{H}_\bullet^{S^1}(LM)$ controlled by four ribbon hypergraphs explicitlyshown in this paper.

Prop of ribbon hypergraphs and strongly homotopy involutive Lie bialgebras