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Leaps: an approach to the block structure of a graph

Henry Martyn Mulder, Ladislav Nebeský (2006)

Discussiones Mathematicae Graph Theory

To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V. These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define the operation + G as well as the set of leaps L G of the connected graph G. The underlying graph of + G , as well...

Local-global convergence, an analytic and structural approach

Jaroslav Nešetřil, Patrice Ossona de Mendez (2019)

Commentationes Mathematicae Universitatis Carolinae

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global convergence to graphs with unbounded degrees. As an application, we extend previous results on continuous clustering of local convergent sequences and prove the existence of modeling quasi-limits for local-global convergent sequences of nowhere dense graphs.

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