Florian Zickfeld

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In this paper we study connections between planar graphs, Schnyder woods, and orthogonal surfaces. Schnyder woods and the face counting approach have important applications in graph drawing and the dimension theory of orders. Orthogonal surfaces explain connections between these seemingly unrelated notions. We use these connections for an intuitive proof of(More)
We deal with the asymptotic enumeration of combinatorial structures on planar maps. Prominent instances of such problems are the enumeration of spanning trees, bipartite perfect matchings, and ice models. The notion of orientations with outdegrees prescribed by a function α : V → N unifies many different combinatorial structures, including the afore(More)
Acknowledgments First of all I want to thank my advisor, Stefan Felsner. In lectures and many discussions I learned a lot from him not only about graph theory and combinatorics. He was also willing to share the large and little tricks and insights that make (scientific) working so much easier. During lunches and many coffee breaks I also learned a lot from(More)
We deal with the enumeration of combinatorial structures on planar maps. Prominent instances of such problems are the enumeration of spanning trees, bipartite perfect matchings and ice models. The notion of an α-orientation unifies many different combinatorial structures, including the afore mentioned. We ask for the number of α-orientations and also for(More)
It is known that graphs on n vertices with minimum degree at least 3 have spanning trees with at least n/4 + 2 leaves and that this can be improved to (n + 4)/3 for cubic graphs without the diamond K4 − e as a subgraph. We generalize the second result by proving that every graph with minimum degree at least 3, without diamonds and certain subgraphs called(More)
It is known that graphs on n vertices with minimum degree at least 3 have spanning trees with at least n/4 + 2 leaves and that this can be improved to (n + 4)/3 for cubic graphs without the diamond K4 −e as a subgraph.We generalize the second result by proving that every graphGwithout diamonds and certain subgraphs called blossomshas a spanning tree with at(More)
I have worked on the problems presented in this section with Stefan Felsner. A paper [8] is a available on the arXiv and a conference version [9] has been submitted. I will now outline what type of questions we consider and our main results. The concept of orientations with fixed out-degrees or α-orientations is a quite general one as we will see below. Let(More)