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Covering a hypergraph of subgraphs

Noga Alon
2002 Discrete Mathematics  
Let G be a tree and let H be a collection of subgraphs of G, each having at most d connected components.  ...  Let ν(H) denote the maximum number of members of H no two of which share a common vertex, and let τ (H) denote the minimum cardinality of a set of vertices of G that intersects all members of H.  ...  For each subgraph H ∈ H let H be the subgraph of T induced on all vertices i ∈ I for which X i contains a vertex of H. Let H denote the set of all subgraphs H of T obtained in this way.  ... 
doi:10.1016/s0012-365x(02)00427-2 fatcat:jekovy4vhrburlkshmbtr6joym

New Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs [chapter]

Arthur H. Busch, Feodor F. Dragan, R. Sritharan
2010 Lecture Notes in Computer Science  
the co-chordal subgraphs of a minimum cover can be found in polynomial time.  ...  Motivated by our use of hypergraphs, we define a class of hypergraphs which lies strictly in between the well studied classes of acyclic hypergraphs and normal hypergraphs.  ...  Acknowledges support from the University of Dayton Research Institute. Acknowledges support from The National Security Agency, USA.  ... 
doi:10.1007/978-3-642-17461-2_17 fatcat:kftdc5kse5bs3g6cpmj4ol56ry

Erdős-Pyber theorem for hypergraphs and secret sharing [article]

László Csirmaz, Péter Ligeti, Gábor Tardos
2013 arXiv   pre-print
We show that these latter constants cannot be improved by more than a factor of 1.89 even for fractional covering by arbitrary complete multipartite subgraphs or subhypergraphs.  ...  A new, constructive proof with a small explicit constant is given to the Erdős-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that  ...  Acknowledgment This research has been partially supported by the Lendület program of the Hungarian Academy of Sciences.  ... 
arXiv:1311.5027v1 fatcat:gzezuksqo5ajvpob3ov5btvfcm

Page 4117 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
A graph G = (Vg, Eg) with Vc Vy is called a realization of the hypergraph H if for any edge e € Ey the corresponding induced subgraph G(e) of G is connected.  ...  The minimum cardinality of a graphoidal cover of G is called the graphoidal covering number of G and is denoted by 4.  ... 

Erdős–Pyber Theorem for Hypergraphs and Secret Sharing

László Csirmaz, Péter Ligeti, Gábor Tardos
2014 Graphs and Combinatorics  
We show that these latter constants cannot be improved by more than a factor of 1.89 even for fractional covering by arbitrary complete multipartite subgraphs or subhypergraphs.  ...  A new, constructive proof with a small explicit constant is given to the Erdős-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that  ...  Acknowledgment This research has been partially supported by the Cryptography Lendület program of the Hungarian Academy of Sciences.  ... 
doi:10.1007/s00373-014-1448-7 fatcat:fii7pzkli5aozdnmp32v4gbmk4

Page 4824 of Mathematical Reviews Vol. , Issue 83m [page]

1983 Mathematical Reviews  
The authors extend in some sense to intersection graphs of some hypergraphs Beineke’s theorem which characterizes line-graphs of graphs by excluding a finite family of induced subgraphs.  ...  The graph covering number of G by G,,G;,---,G, is the number of k-tuples (G{, G3,--+,G,) that cover G and have G/ isomorphic to G; for each i=1,2,---,k.  ... 

On Intersection Graphs of Graphs and Hypergraphs: A Survey [article]

Ranjan N. Naik
2019 arXiv   pre-print
The theory of intersection graphs of hypergraphs has been a classical topic in the theory of special graphs.  ...  Keywords: Hypergraphs, Intersection graphs, Line graphs, Representative graphs, Derived graphs, Algorithms (ALG), Forbidden induced subgraphs (FIS), Krausz partitions, Eigenvalues.  ...  In [20] , [21] , [23] , [24] , [25] , [26] , [28] , [29] , [36] , [37] and [38] , it is well noted that if G has a linear -covering, then the covering must contain the set of all subgraphs  ... 
arXiv:1809.08472v4 fatcat:nssumxcd2zavhhkaifbumxy6uy

Incidence graphs of biacyclic hypergraphs

Feodor F. Dragan, Vitaly I. Voloshin
1996 Discrete Applied Mathematics  
It is well-known that the incidence graphs of totally balanced hypergraphs are exactly chordal bipartite graphs. This paper examines the incidence graphs of biacyclic hypergraphs.  ...  Acknowledgments We are grateful to the anonymous referee for improving the representation of this paper.  ...  A hypergraph is conformaI if every clique (= maximal complete subgraph) of its underlying graph is contained in an edge of H.  ... 
doi:10.1016/0166-218x(95)00070-8 fatcat:e6mo72i6nvdx7azguvyslh4fum

Regular subgraphs of uniform hypergraphs

Jaehoon Kim
2016 Journal of combinatorial theory. Series B (Print)  
Moreover, if r∈{3,4}, r| k and k,n are both sufficiently large, then the maximum number of edges in an n-vertex k-uniform hypergraph containing no r-regular subgraphs is exactly n-1k-1, with equality only  ...  if all edges contain a specific vertex v.  ...  The author especially thanks one referee for teaching him the current proof of Theorem 1.2 which is much better than the proof in the old version and yields better bound on k.  ... 
doi:10.1016/j.jctb.2016.03.001 fatcat:zfun5nivdjgwnbmxpmcoxbadsq

Independent sets in bounded-degree hypergraphs

Magnús M. Halldórsson, Elena Losievskaja
2009 Discrete Applied Mathematics  
This technique allows us to show that the greedy algorithm for MIS that corresponds to the classical greedy set cover algorithm has a performance ratio of (∆ + 1)/2.  ...  For MSIS, we give two variations of the basic greedy algorithm and describe a family of hypergraphs where both algorithms approach the bound of ∆.  ...  Part of a hard 3-regular 4-uniform hypergraph for GreedyN, where one of the first r − 1 subgraphs is connected to the last subgraph.  ... 
doi:10.1016/j.dam.2008.11.013 fatcat:grgz5d2q5fbhba7rlrklshfy24

Page 5943 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
The H-covering number C(H,G) [H-packing number P(H, G)] of G is the size of a smallest H-covering [largest H-packing] of G.  ...  A split graph is a graph whose vertex set can be partitioned into two disjoint parts, where one induces a totally disconnected subgraph and the other a complete subgraph.  ... 

Graded Sparse Graphs and Matroids [article]

Audrey Lee, Ileana Streinu, Louis Theran
2007 arXiv   pre-print
Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of generically rigid structures.  ...  We define a new family called graded sparse graphs, arising from generically pinned (completely immobilized) bar-and-joint frameworks and prove that they also form matroids.  ...  This research was supported by the NSF CCF 0728783 grant of Ileana Streinu.  ... 
arXiv:0711.2838v2 fatcat:4xsqpazgajc7xekubmxt3q3owe

Page 5478 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
Let & denote a collection of complete bipartite subgraphs of a graph G = (V,E), and let |@| denote the cardinality of @. & is said to cover G if E equals the union of the edge sets of members of @.  ...  98i:05123 lant graphs and join-graphs of a hypergraph.  ... 

Page 1653 of Mathematical Reviews Vol. , Issue 81E [page]

1981 Mathematical Reviews  
The author characterizes n-fold covers and multiple group covers of hypergraphs independent of a covering projection.  ...  For several binary and unary operations on hypergraphs it is shown that the application to an n-fold cover (a group cover) yields an n-fold cover.  ... 

Neighborhood perfect graphs

J Lehel, Zs Tuza
1986 Discrete Mathematics  
of vertices whose neighborhood subgraphs cover the edge set of G.  ...  Let G be a graph, ~N(G) denote the maximum number of edges such that no two of them belong to the same subgraph of G induced by the (closed) neighborhood of some vertex; let PN(G) be the minimum number  ...  Acknowledgment The authors wish to express their gratitude to one of the referees for the helpful remarks.  ... 
doi:10.1016/0012-365x(86)90031-2 fatcat:mpzq2gxdeza4pblnxauukpmu64
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