Ehrenfeucht, A.; Rozenberg, G. Theory of 2-structures. II: Representation through labeled tree families. (English) Zbl 0701.05052 Theor. Comput. Sci. 70, No. 3, 305-342 (1990). This paper continues the investigation of the theory of 2-structures initiated in Part I (see [Zbl 0701.05051]). Hierarchical representations of 2-structures through 2s-labeled tree families are studied. The main result states that every 2-structure is, in fact, a 2s-labeled family of primitive, complete or linear 2-structures. Hence, each 2- structure can be decomposed into primitive, complete and linear 2-structures. Given a 2-structure \((D,R)\). Denote by \(2^ D\) the set of all subsets of \(D\). For \(X,Y\in 2^ D\), \(X\), \(Y\) are overlapping if \(X\setminus Y\neq \emptyset\), \(Y\setminus X\neq \emptyset\), \(X\cap Y\neq \emptyset\).A 2s-labeled tree family is a triple \((D,{\mathcal F},\phi)\), where \(D\) is a finite set, \({\mathcal F}\subseteq 2^ D\) such that \(D\in {\mathcal F}\), \(\emptyset \not\in {\mathcal F}\), \(\{x\}\in {\mathcal F}\) for every \(x\in D\), for every \(X,Y\in {\mathcal F}\), \(X\), \(Y\) are not overlapping and \(\phi (X)\) is a 2-structure for every \(X\in {\mathcal F}\). Reviewer: Marie Demlová (Praha) Cited in 4 ReviewsCited in 35 Documents MSC: 05C99 Graph theory 05C05 Trees 68R10 Graph theory (including graph drawing) in computer science Keywords:decomposition; 2-structures; 2s-labeled tree families Citations:Zbl 0701.05051 PDFBibTeX XMLCite \textit{A. Ehrenfeucht} and \textit{G. Rozenberg}, Theor. Comput. Sci. 70, No. 3, 305--342 (1990; Zbl 0701.05052) Full Text: DOI References: [1] Berge, C., Graphs and Hypergraphs (1983), North-Holland: North-Holland Amsterdam · Zbl 0523.05040 [2] Ehrenfeucht, A.; Rozenberg, G., Theory of 2-structures, Part I: clans, basic subclasses, and morphisms, Theoret. Comput. Sci., 70, 277-303 (1990), (this issue) · Zbl 0701.05051 [3] Ehrenfeucht, A.; Rozenberg, G., Primitivity is hereditary for 2-structures, Theoret. Comput. Sci., 70, 343-358 (1990), (this issue) · Zbl 0701.05053 [4] (Ehrig, H.; Nagl, M.; Rozenberg, G.; Rosenfeld, A., Graph Grammars and their Application to Computer Science (1987), Springer: Springer Berlin) · Zbl 0636.00013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.