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Transversals and Independence in Linear Hypergraphs with Maximum Degree Two

Michael A. Henning, Anders Yeo
2017 Electronic Journal of Combinatorics  
For $k \ge 2$, let $H$ be a $k$-uniform hypergraph on $n$ vertices and $m$ edges. Let $S$ be a set of vertices in a hypergraph $H$.  ...  In this paper, we prove a much more powerful result, and establish tight upper bounds on $\tau(H)$ and tight lower bounds on $\alpha(H)$ that are achieved for infinite families of hypergraphs.  ...  If a vertex x ∈ T covers only one hyperedge in H that is not covered by T \ {x}, then delete this vertex from T and the edge it covers from H.  ... 
doi:10.37236/6160 fatcat:wh6pdv6nu5govgzf22q2xephnu

Connection Matrices for MSOL-Definable Structural Invariants [chapter]

Johann Makowsky
2008 Lecture Notes in Computer Science  
Connection matrices of graph parameters were first introduced by M. Freedman, L. Lovász and A.  ...  In this talk we discuss several applications of this Finite Rank Theorem, and outline ideas for further research.  ...  Kotek for their contributions in [GKM08] , to T. Kotek who allowed me to include his Proposition 10 from his thesis work, to L. Lyaudet for proof reading these notes, and to L. Lovász and A.  ... 
doi:10.1007/978-3-540-92701-3_4 fatcat:mij5fisswbdafjshrkbyygjita

Resolutions of Convex Geometries

Domenico Cantone, Jean-Paul Doignon, Alfio Giarlotta, Stephen Watson
2021 Electronic Journal of Combinatorics  
Contrary to what happens for similar constructions–compounds of hypergraphs, as in Chein, Habib and Maurer (1981), and compositions of set systems, as in Möhring and Radermacher)–, resolutions of convex  ...  A notion of primitivity, which generalize the corresponding notion for posets, arises from resolutions: a convex geometry is primitive if it is not a resolution of smaller ones.  ...  They are also grateful to Davide Carpentiere for several useful discussions on the topic, and Pierre Ille for relevant information on primitive posets.  ... 
doi:10.37236/10328 fatcat:g26qlsvezrg6fn7xz3no4rb7sa

Complexity Measures on the Symmetric Group and Beyond [article]

Neta Dafni, Yuval Filmus, Noam Lifshitz, Nathan Lindzey, Marc Vinyals
2020 arXiv   pre-print
To add sensitivity to the mix, we reduce to Huang's sensitivity theorem using "pseudo-characters", which witness the degree of a function.  ...  As another application of our ideas, we simplify the characterization of maximum-size t-intersecting families in the symmetric group and the perfect matching scheme.  ...  The domain consists of all |λ|-uniform hypermatchings in the complete "λ-partite" hypergraph on |λ|n vertices.  ... 
arXiv:2010.07405v1 fatcat:uhfeqpugxnfyjh5sekdwjayrxi

Combinatorial Gray codes-an updated survey [article]

Torsten Mütze
2022 arXiv   pre-print
This survey provides a comprehensive picture of the state-of-the-art of the research on combinatorial Gray codes. In particular, it gives an update on Savage's influential survey [C. D. Savage.  ...  A combinatorial Gray code for a class of objects is a listing that contains each object from the class exactly once such that any two consecutive objects in the list differ only by a 'small change'.  ...  Her construction uses Baranyai's well-known partition theorem for complete hypergraphs.  ... 
arXiv:2202.01280v2 fatcat:qq3apclxafbhzazbfcu45n4kue

Extremal Hypergraphs for Ryser's Conjecture [article]

Lothar Narins, Universitätsbibliothek Der FU Berlin, Universitätsbibliothek Der FU Berlin
The proof of this theorem that one finds in the literature is rather algebraic. We give a more geometric proof using certain triangulation techniques.  ...  A theorem of Meshulam that concerns the connectedness of the independence complex of a graph plays an important role in our proofs.  ...  In it, we find a lower bound on the connectedness of the independence complex of line graphs in terms of the vertex cover number of the hypergraph.  ... 
doi:10.17169/refubium-17678 fatcat:ipa2qcuo45ab5fb644qtxcpbea

Solving linear programs on factorized databases [article]

Florent Capelli, Nicolas Crosetti, Joachim Niehren, Jan Ramon
2019 arXiv   pre-print
When the data is extracted using a query on a database, this approach ignores the underlying structure of the answer set which may result in a blow-up of the size of the linear program if the answer set  ...  A typical workflow for solving a linear programming problem is to first write a linear program parametrized by the data in a language such as Math GNU Prog or AMPL then call the solver on this program  ...  of the Conseil Rgional Hauts-de-France.  ... 
arXiv:1901.03633v2 fatcat:gwqfhrk7wzfktol6uymt4d3wqi

On algorithms for large-scale graph and clustering problems

Chris Schwiegelshohn, Technische Universität Dortmund, Technische Universität Dortmund
Dabei ist der Jaccard Index |A ∩ B|/|A U B| das Ähnlichkeitsmaß für zwei Mengen A und B.  ...  In der Arbeit wird eine Datenstruktur beschrieben, die dies erstmalig in dynamischen Datenströmen mit geringem Speicherplatzverbrauch leistet.  ...  Given a graph G(V, E), a vertex cover is a set K ⊂ V such that e ∩ K = ∅ for any e ∈ E. The minimum vertex cover is the vertex cover of smallest cardinality. Theorem 6.4.2.  ... 
doi:10.17877/de290r-18125 fatcat:4d2qqsphbbfldpqsydar7sutjq

Algorithmic Contributions to Computational Molecular Biology Algorithmic Contributions to Computational Molecular Biology Soutenue publiquement le 1 Juin 2010 devant le jury compos de

Stéphane Vialette, Gregory Kucherov
The early work of Johnson [Johnson, 1974] and Lovász [Lovász, 1974] on the MINIMUM SET COVER problem pioneered the greedy analysis approach, while Chvátal [Chvátal, 1979] gave the first analysis  ...  Given a partition P of a string u and a partition Q of a string v, the pair (P, Q) is a common partition of u and v if Q is a permutation of P.  ... 

Reinforcement Learning (Dagstuhl Seminar 13321) The Critical Internet Infrastructure (Dagstuhl Seminar 13322) Coding Theory (Dagstuhl Seminar 13351) Interaction with Information for Visual Reasoning (Dagstuhl Seminar 13352)

Peter Auer, Marcus Hutter, Laurent, Georg Carle, Jochen Schiller, Steve Uhlig, Walter Willinger, Matthias Wählisch, Thore Husfeldt, Ramamohan Paturi, Gregory Sorkin, Ryan Williams (+14 others)
Mark: THink of a whirlpool engineer, modern washing machines considers chemicals, mechanical etc. aspects. Is there a lesson for biology? Anja: We are working in this area.  ...  Alex: Flow Cytometry data analysis is a real case of Big-Data robots producing much larger data than can be processed at the moment.  ...  The partition matrix has rows and columns indexed by the partitions of t elements; all entries are 1 or 0 depending on whether the meet of the two indexing partitions gives the unit partition.  ...