Author
Philipp Sprüssel
Other affiliations: University of Hamburg
Bio: Philipp Sprüssel is an academic researcher from Graz University of Technology. The author has contributed to research in topics: Singular homology & Hitting time. The author has an hindex of 11, co-authored 43 publications receiving 320 citations. Previous affiliations of Philipp Sprüssel include University of Hamburg.
Papers
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TL;DR: It is proved that under this condition H must have a perfect matching, which answers a question of Kuhn and Osthus.
Abstract: Let H be an r-partite r-graph, all of whose sides have the same size n. Suppose that there exist two sides of H, each satisfying the following condition: the degree of each legal r-1-tuple contained in the complement of this side is strictly larger than n2. We prove that under this condition H must have a perfect matching. This answers a question of Kuhn and Osthus.
56 citations
TL;DR: In this paper, Diestel et al. present a survey of the topological approach to the study of locally finite graphs with ends, where topological arcs and circles are assumed to play the role played in finite graphs by paths and cycles.
36 citations
TL;DR: In this paper, the Max-Flow Min-Cut theorem for countable networks was shown to hold for locally finite networks, where the flow saturates the cut and is zero on the reverse cut.
28 citations
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TL;DR: In this paper, it was shown that the topological cycle space of a locally finite graph G is generated by its geodetic topological circles, and that although the finite cycles of G generate C(G), its finite geodic cycles need not generate G(G).
Abstract: We prove that the topological cycle space C(G) of a locally finite graph G is generated by its geodetic topological circles. We further show that, although the finite cycles of G generate C(G), its finite geodetic cycles need not generate C(G).
20 citations
TL;DR: It is proved that every rayless graph has an unfriendly partition and the inequality of the following type is fixed: Every graph has at least one partition that is notriendly.
Abstract: It is proved that every graph containing no infinite path has an unfriendly partition.
17 citations
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TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.
7,116 citations
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TL;DR: In this paper, the authors pointed out that the distinction between "finite" and "infinite" is one which does not require definition, and that the authors' view is not the only accepted view.
Abstract: THE criticism on the passage quoted from p. 3 of the book by Profs. Harkness and Morley (NATURE, February 23, p. 347) turns on the fact that, in dealing with number divorced from measurement, the authors have used the phrase “an infinity of objects” without an explicit statement of its meaning. I am not sure that I understand the passage in their letter which refers to this point; but it seems to me to imply that the distinction between “finite” and “infinite” is one which does not require definition. This is not the only accepted view. It is not, for instance, the view taken in Herr Dedekind's book, “Was sind und was sollen die Zahlen.” As regards the opening sentences of Chapter xv., the authors have apparently misunderstood the point of my objection. With the usually received definition of convergence of an infinite product, Π(1-αn), if convergent, is different from zero. So far as the passage quoted goes, Π(1-αn) might be zero; and it is therefore not shown to be convergent, if the usual definition of convergence be assumed. As to the passage quoted from p. 232, I must express to the authors my regret for having overlooked the fact that the particular rearrangement, there made use of, has been fully justified in Chapter viii. Whether Log x is or is not, at the beginning of Chapter iv., defined by means of a string and a cone, will be obvious to any one who will read the whole passage (p. 46, line 16, to p. 47, line 9) leading up to the definition.
740 citations
TL;DR: A newly developed ''absorbing'' technique is employed, which has a potential to be applicable in a more general context of establishing existence of spanning subgraphs of graphs and hypergraphs.
178 citations
TL;DR: In this article, the authors give an overview of recent progress in F-packings, with the main emphasis on F-packing, Hamiltonicity problems and tree embeddings, and describe some of the methods involved.
Abstract: What conditions ensure that a graph G contains some given spanning subgraph H? The most famous examples of results of this kind are probably Dirac's theorem on Hamilton cycles and Tutte's theorem on perfect matchings. Perfect matchings are generalized by perfect F-packings, where instead of covering all the vertices of G by disjoint edges, we want to cover G by disjoint copies of a (small) graph F. It is unlikely that there is a characterization of all graphs G which contain a perfect F-packing, so as in the case of Dirac's theorem it makes sense to study conditions on the minimum degree of G which guarantee a perfect F-packing.
The Regularity lemma of Szemeredi and the Blow-up lemma of Komlos, Sarkozy and Szemeredi have proved to be powerful tools in attacking such problems and quite recently, several long-standing problems and conjectures in the area have been solved using these. In this survey, we give an outline of recent progress (with our main emphasis on F-packings, Hamiltonicity problems and tree embeddings) and describe some of the methods involved.
176 citations
01 Jan 2010
TL;DR: A survey of the state-of-the-art for perfect matchings in hypergraphs can be found in this article, where the authors present the current state of the art and pose some open problems.
Abstract: Dedicated to Endre Szemeredi on the occasion of his 70th birthday In 1952 Dirac [8] proved a celebrated theorem stating that if the minimum degree δ(G) in an n-vertex graph G is at least n/2 then G contains a Hamiltonian cycle. In 1999, Katona and Kierstead initiated a new stream of research devoted to studying similar questions for hypergraphs, and subsequently, for perfect matchings. A pivotal role in achieving some of the most important results in both these areas was played by Endre Szemeredi. In this survey we present the current state-of-art and pose some open problems.
167 citations