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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.

Localization of jumps of the point-distinguishing chromatic index of K n , n

Mirko Horňák, Roman Soták (1997)

Discussiones Mathematicae Graph Theory

The point-distinguishing chromatic index of a graph represents the minimum number of colours in its edge colouring such that each vertex is distinguished by the set of colours of edges incident with it. Asymptotic information on jumps of the point-distinguishing chromatic index of K n , n is found.

Locally bounded k-colorings of trees

C. Bentz, C. Picouleau (2009)

RAIRO - Operations Research

Given a tree T with n vertices, we show, by using a dynamic programming approach, that the problem of finding a 3-coloring of T respecting local (i.e., associated with p prespecified subsets of vertices) color bounds can be solved in O(n6p-1logn) time. We also show that our algorithm can be adapted to the case of k-colorings for fixed k.

Locally regular graphs

Bohdan Zelinka (2000)

Mathematica Bohemica

A graph G is called locally s -regular if the neighbourhood of each vertex of G induces a subgraph of G which is regular of degree s . We study graphs which are locally s -regular and simultaneously regular of degree r .

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