318 research outputs found
Automorphism Groups of Geometrically Represented Graphs
We describe a technique to determine the automorphism group of a
geometrically represented graph, by understanding the structure of the induced
action on all geometric representations. Using this, we characterize
automorphism groups of interval, permutation and circle graphs. We combine
techniques from group theory (products, homomorphisms, actions) with data
structures from computer science (PQ-trees, split trees, modular trees) that
encode all geometric representations.
We prove that interval graphs have the same automorphism groups as trees, and
for a given interval graph, we construct a tree with the same automorphism
group which answers a question of Hanlon [Trans. Amer. Math. Soc 272(2), 1982].
For permutation and circle graphs, we give an inductive characterization by
semidirect and wreath products. We also prove that every abstract group can be
realized by the automorphism group of a comparability graph/poset of the
dimension at most four
Combinatorial Problems on -graphs
Bir\'{o}, Hujter, and Tuza introduced the concept of -graphs (1992),
intersection graphs of connected subgraphs of a subdivision of a graph .
They naturally generalize many important classes of graphs, e.g., interval
graphs and circular-arc graphs. We continue the study of these graph classes by
considering coloring, clique, and isomorphism problems on -graphs.
We show that for any fixed containing a certain 3-node, 6-edge multigraph
as a minor that the clique problem is APX-hard on -graphs and the
isomorphism problem is isomorphism-complete. We also provide positive results
on -graphs. Namely, when is a cactus the clique problem can be solved in
polynomial time. Also, when a graph has a Helly -representation, the
clique problem can be solved in polynomial time. Finally, we observe that one
can use treewidth techniques to show that both the -clique and list
-coloring problems are FPT on -graphs. These FPT results apply more
generally to treewidth-bounded graph classes where treewidth is bounded by a
function of the clique number
Automorphism Groups of Geometrically Represented Graphs
Interval graphs are intersection graphs of closed intervals and circle graphs are intersection graphs of chords of a circle. We study automorphism groups of these graphs. We show that interval graphs have the same automorphism groups as trees, and circle graphs have the same
as pseudoforests, which are graphs with at most one cycle in every connected component.
Our technique determines automorphism groups for classes with a
strong structure of all geometric representations, and it can be applied to other graph classes. Our results imply polynomial-time algorithms for computing automorphism groups in term of group products
On the Weisfeiler-Leman dimension of some polyhedral graphs
Let be a positive integer, a graph with vertex set , and
the coloring of the Cartesian -power , obtained by
the -dimensional Weisfeiler-Leman algorithm. The -dimension of the
graph is defined to be the smallest for which the coloring determines up to isomorphism. It is known that the -dimension of any planar graph is or , but no planar graph of -dimension is known. We prove that the -dimension of a
polyhedral (i.e., -connected planar) graph is at most if the color
classes of the coloring are the orbits of the componentwise
action of the group on
Ältere Migranten in Deutschland: Befunde zur soziodemographischen, sozioökonomischen und psychosozialen Lage sowie zielgruppenbezogene Fragen der Politik- und Praxisfeldentwicklung ; Expertise im Auftrag des Bundesamtes für Flüchtlinge und Migration
Die Expertise reflektiert kritisch die Forschungssituation zu älteren Migranten in Deutschland. Hierzu werden die Befunde vorliegender Studien mit Ergebnissen des DZA-Alterssurvey 2002 zusammengeführt. Behandelt werden u.a. sozialstrukturelle Merkmale der älteren Migranten, Befunde zur Lebenslage, Rückkehrabsichten und Prozesse der Transmigration sowie der Bedarf an Pflegeleistungen. Abschließend werden Desiderata der Forschung aufgelistet. (BAMF
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