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Transversals and Independence in Linear Hypergraphs with Maximum Degree Two

2017
*
Electronic Journal of Combinatorics
*

For $k \ge 2$, let $H$ be

doi:10.37236/6160
fatcat:wh6pdv6nu5govgzf22q2xephnu
*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. ...##
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Connection Matrices for MSOL-Definable Structural Invariants
[chapter]

2008
*
Lecture Notes in Computer Science
*

Connection matrices

doi:10.1007/978-3-540-92701-3_4
fatcat:mij5fisswbdafjshrkbyygjita
*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*. ...##
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Resolutions of Convex Geometries

2021
*
Electronic Journal of Combinatorics
*

Contrary to what happens for similar constructions–compounds

doi:10.37236/10328
fatcat:g26qlsvezrg6fn7xz3no4rb7sa
*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. ...##
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Complexity Measures on the Symmetric Group and Beyond
[article]

2020
*
arXiv
*
pre-print

To add sensitivity to the mix, we reduce to Huang's sensitivity

arXiv:2010.07405v1
fatcat:uhfeqpugxnfyjh5sekdwjayrxi
*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. ...##
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Combinatorial Gray codes-an updated survey
[article]

2022
*
arXiv
*
pre-print

This survey provides

arXiv:2202.01280v2
fatcat:qq3apclxafbhzazbfcu45n4kue
*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*. ...##
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Extremal Hypergraphs for Ryser's Conjecture
[article]

2015

The proof

doi:10.17169/refubium-17678
fatcat:ipa2qcuo45ab5fb644qtxcpbea
*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*. ...##
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Solving linear programs on factorized databases
[article]

2019
*
arXiv
*
pre-print

When the data is extracted using

arXiv:1901.03633v2
fatcat:gwqfhrk7wzfktol6uymt4d3wqi
*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. ...##
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On algorithms for large-scale graph and clustering problems

2017

Dabei ist der Jaccard Index |

doi:10.17877/de290r-18125
fatcat:4d2qqsphbbfldpqsydar7sutjq
*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. ...##
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Algorithmic Contributions to Computational Molecular Biology Algorithmic Contributions to Computational Molecular Biology Soutenue publiquement le 1 Juin 2010 devant le jury compos de

unpublished

The early work

fatcat:fkvaousvmfgw3d7hxsaradaixi
*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. ...##
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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)

unpublished

Mark: THink

fatcat:iz3co5xisfejfbnx2t6ptrorfm
*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*. ...