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## Filters

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Covering a hypergraph of subgraphs

2002
*
Discrete Mathematics
*

Let G be

doi:10.1016/s0012-365x(02)00427-2
fatcat:jekovy4vhrburlkshmbtr6joym
*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. ...##
###
New Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

the co-chordal

doi:10.1007/978-3-642-17461-2_17
fatcat:kftdc5kse5bs3g6cpmj4ol56ry
*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. ...##
###
Erdős-Pyber theorem for hypergraphs and secret sharing
[article]

2013
*
arXiv
*
pre-print

We show that these latter constants cannot be improved by more than

arXiv:1311.5027v1
fatcat:gzezuksqo5ajvpob3ov5btvfcm
*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. ...##
###
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. ...

##
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Erdős–Pyber Theorem for Hypergraphs and Secret Sharing

2014
*
Graphs and Combinatorics
*

We show that these latter constants cannot be improved by more than

doi:10.1007/s00373-014-1448-7
fatcat:fii7pzkli5aozdnmp32v4gbmk4
*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. ...##
###
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]

2019
*
arXiv
*
pre-print

The theory

arXiv:1809.08472v4
fatcat:nssumxcd2zavhhkaifbumxy6uy
*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*...##
###
Incidence graphs of biacyclic hypergraphs

1996
*
Discrete Applied Mathematics
*

It is well-known that the incidence graphs

doi:10.1016/0166-218x(95)00070-8
fatcat:e6mo72i6nvdx7azguvyslh4fum
*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. ...##
###
Regular subgraphs of uniform hypergraphs

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

doi:10.1016/j.jctb.2016.03.001
fatcat:zfun5nivdjgwnbmxpmcoxbadsq
*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. ...##
###
Independent sets in bounded-degree hypergraphs

2009
*
Discrete Applied Mathematics
*

This technique allows us to show that the greedy algorithm for MIS that corresponds to the classical greedy set

doi:10.1016/j.dam.2008.11.013
fatcat:grgz5d2q5fbhba7rlrklshfy24
*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*. ...##
###
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]

2007
*
arXiv
*
pre-print

Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics

arXiv:0711.2838v2
fatcat:4xsqpazgajc7xekubmxt3q3owe
*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. ...##
###
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

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. ...

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