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Open AccessLattice Path Matroids and Quotients
We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering LPMs by quotients yields a graded poset, whose rank polynomial...
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Article
Open AccessFinitary Affine Oriented Matroids
We initiate the axiomatic study of affine oriented matroids (AOMs) on arbitrary ground sets, obtaining fundamental notions such as minors, reorientations and a natural embedding into the frame work of Complexe...
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Article
Open AccessBeyond symmetry in generalized Petersen graphs
A graph is a core or unretractive if all its endomorphisms are automorphisms. Well-known examples of cores include the Petersen graph and the graph of the dodecahedron—both generalized Petersen graphs. We charact...
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Article
On monoid graphs
We investigate Cayley graphs of finite semigroups and monoids. First, we look at semigroup digraphs, i.e., directed Cayley graphs of semigroups, and give a Sabidussi-type characterization in the case of monoid...
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Article
Chomp on generalized Kneser graphs and others
In Chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning...
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Chapter and Conference Paper
On the Dichromatic Number of Surfaces
In this paper, we give bounds on the dichromatic number \(\overrightarrow{\chi }(\varSigma )\) ...
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Article
Open AccessFlip Distances Between Graph Orientations
Flip graphs are a ubiquitous class of graphs, which encode relations on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilat...
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Article
Enumerating k-Arc-Connected Orientations
We study the problem of enumerating the k-arc-connected orientations of a graph G, i.e., generating each exactly once. A first algorithm using submodular flow optimization is easy to state, but intricate to imple...
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Article
Cayley Posets
We introduce Cayley posets as posets arising naturally from pairs \(S<T\) S < T of semigroups, much in the same way that a Cayley graph arises from a (semi)group and a subset. We show that Cayley posets are...
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Article
On Tope Graphs of Complexes of Oriented Matroids
We give two graph theoretical characterizations of tope graphs of (complexes of) oriented matroids. The first is in terms of excluded partial cube minors, the second is that all antipodal subgraphs are gated. ...
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Chapter and Conference Paper
Plattenbauten: Touching Rectangles in Space
Planar bipartite graphs can be represented as touching graphs of horizontal and vertical segments in \(\mathbb {R}^2\) ...
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Chapter and Conference Paper
Flip Distances Between Graph Orientations
Flip graphs are a ubiquitous class of graphs, which encode relations on a set of combinatorial objects induced by elementary, local changes
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Article
On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial
In this paper we investigate the number of integer points lying in dilations of lattice path matroid polytopes. We give a characterization of such points as polygonal paths in the diagram of the lattice path m...
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Article
How Many Circuits Determine an Oriented Matroid?
Las Vergnas and Hamidoune studied the number of circuits needed to determine an oriented matroid. In this paper we investigate this problem and some new variants, as well as their interpretation in particular ...
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Chapter and Conference Paper
The Queue-Number of Posets of Bounded Width or Height
Heath and Pemmaraju [9] conjectured that the queue-number of a poset is bounded by its width and if the poset is planar then also by its height. We show that there are planar posets whose queue-number is larger t...
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Article
On the Duality of Semiantichains and Unichain Coverings
We study a min-max relation conjectured by Saks and West: For any two posets P and Q the size of a maximum semiantichain and the size of a minimum unichain covering in the product P×Q are equal. As a positive res...
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Article
On planar right groups
In 1896 Heinrich Maschke characterized planar finite groups, that is groups which admit a generating system such that the resulting Cayley graph is planar. In our study we consider the question, which finite semi...
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Chapter and Conference Paper
Graph Drawings with One Bend and Few Slopes
We consider drawings of graphs in the plane in which edges are represented by polygonal paths with at most one bend and the number of different slopes used by all segments of these paths is small. We prove that ...
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Book
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Chapter
Ringe und Moduln
In diesem Kapitel befassen wir uns noch mal intensiver mit den in den vorangegangenen Kap. 7 und 8 schon untersuchten Ringen und Moduln. Diese stellen einen wichtigen Zweig in der sogenannten Modernen Algebra ...
