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Size of k-uniform hypergraph with diameter d

2003
*
Discrete Mathematics
*

In this paper, we estimate the

doi:10.1016/s0012-365x(02)00593-9
fatcat:7hzv7az37bblhcqjfzxcblqfcu
*size**of**k*-*uniform**hypergraph**with**diameter**d*, and give its minimum and maximum. ... Furthermore, we give an exact estimation about the*size**of**k*-*uniform**hypergraph**with**diameter**d*and order n, that is a generalization*of*a result [3]*of*Ore's. ... Replacing*d*(H )6d*with**d*(H )=*d*, we obtain another parameter m (*d*;*k*; n)= min{s(H ) |*d*(H )=*d*; o(H )=n; H is*k*-*uniform*}. It is the smallest*size**of*a*k*-*uniform**hypergraph**with**diameter**d*and order n. ...##
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On the transmission of uniform unicyclic hypergraphs
[article]

2018
*
arXiv
*
pre-print

We determine the unique

arXiv:1808.09962v2
fatcat:5vqrv5cbrjhwfirhgxgp33jskq
*uniform*unicyclic*hypergraphs**of*fixed*size**with*minimum and maximum transmissions, respectively. ... The transmission*of*a connected*hypergraph*is defined as the summation*of*distances between all unordered pairs*of*distinct vertices. ... In the following, we determine the unique*hypergraphs**with*maximum transmission in the set*of**k*-*uniform*unicyclic*hypergraphs**of*fixed*size*for*k*≥ 3. Lemma 4. ...##
###
Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number

2021
*
Discrete Dynamics in Nature and Society
*

We show that balanced hyperbugs maximize the spectral radii

doi:10.1155/2021/5805239
fatcat:qpyzeammazcavpkwgtr7wybpuu
*of**hypergraphs**with*fixed number*of*vertices and*diameter*and kite*hypergraphs*minimize the spectral radii*of**hypergraphs**with*fixed number*of*... In this paper, we defined two classes*of**hypergraphs*, hyperbugs and kite*hypergraphs*. ... Acknowledgments is study was partially supported by the National Natural Science Foundation*of*China (grant no. 11551003), the Natural Science Foundation*of*Guangdong Province (grant no. 2021A1515012045 ...##
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The largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)
[article]

2018
*
arXiv
*
pre-print

Let S(m,

arXiv:1807.05955v2
fatcat:srgyutysknf6xef5jbudkbhv6i
*d*,*k*) be the set*of**k*-*uniform*supertrees*with*m edges and*diameter**d*and q(G) be the signless Laplacian spectral radius*of*a*k*-*uniform**hypergraph*G. ... Let S_1(m,*d*,*k*) be the*k*-*uniform*supertree obtained from a loose path P:v_1, e_1, v_2, ...,v_d, e_d, v_d+1*with*length*d*by attaching m-*d*edges at vertex v_d/2+1. ... [19] determine the first ⌊*d*2 ⌋ + 1 largest spectral radii*of**k*-*uniform*supertrees*with**size*m and*diameter**d*and the first two smallest spectral radii*of*supertrees*with**size*m by using the methods ...##
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The matching polynomials and spectral radii of uniform supertrees
[article]

2018
*
arXiv
*
pre-print

Using the methods

arXiv:1807.01180v1
fatcat:elbnrsdttjgrtnr6mogvwo2xsq
*of*grafting operations on supertrees and comparing matching polynomials*of*supertrees, we determine the first*d*/2+1 largest spectral radii*of*r-*uniform*supertrees*with**size*m and*diameter*... We study matching polynomials*of**uniform**hypergraph*and spectral radii*of**uniform*supertrees. ...*size*m and*diameter**d*in Section 5. ...##
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The Matching Polynomials and Spectral Radii of Uniform Supertrees

2018
*
Electronic Journal of Combinatorics
*

*with*

*size*$m$ and

*diameter*$

*d*$. ... We study matching polynomials

*of*

*uniform*

*hypergraph*and spectral radii

*of*

*uniform*supertrees. ... spectral radii

*of*supertrees among all r-

*uniform*supertrees

*with*

*size*m and

*diameter*

*d*in Section 5. ...

##
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Decompositions into Subgraphs of Small Diameter

2010
*
Combinatorics, probability & computing
*

Let P (n, ,

doi:10.1017/s0963548310000040
fatcat:pgfnioyhxzgsdfzwivqdj7357u
*d*) be the smallest*k*such that every graph G = (V , E) on n vertices has an edge partition E = E 0 ∪ E 1 ∪ · · · ∪ E*k*such that |E 0 | n 2 , and for all 1 i*k*the*diameter**of*the subgraph ... Finally, we extend some*of*these results to*hypergraphs*, improving earlier work*of*Polcyn, Rödl, Ruciński and Szemerédi. ... Let*K*(t;*k*) denote the complete*k*-partite*k*-*uniform**hypergraph**with*parts*of**size*t, whose edges are all the*k*-sets which intersect every part in one vertex. ...##
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On the spectrum and linear programming bound for hypergraphs
[article]

2022
*
arXiv
*
pre-print

We also determine the largest order

arXiv:2009.03022v2
fatcat:pdteabgphnbobfe7ukambxvktq
*of*an r-regular u-*uniform**hypergraph**with*second eigenvalue at most θ for several parameters (r,u,θ). ... In this paper, we extend previous work done for graphs and bipartite graphs and present a linear programming method for obtaining an upper bound on the order*of*a regular*uniform**hypergraph**with*prescribed ... We are grateful to the two anonymous referees for their comments and suggestions that have greatly improved the first version*of*our paper. ...##
###
Intersecting designs from linear programming and graphs of diameter two

1994
*
Discrete Mathematics
*

The new results presented here are corollaries

doi:10.1016/0012-365x(92)00478-a
fatcat:yew2albzkbhsfcwbjirbb2tctm
*of*a recent improvement about*uniform**hypergraphs**with*maximal fractional matchings. We propose several open problems. ... We investigate l-designs (regular intersecting families) and graphs*of**diameter*2. ... Acknowledgement The author is grateful to the organizers*of*the Second Japan Conference on Graph Theory and Combinatorics, 18-22 August 1990, at Hakone, Japan, where this paper was presented. ...##
###
Minimally Connected Hypergraphs
[article]

2019
*
arXiv
*
pre-print

In this paper, we define a construction process for minimally connected r-

arXiv:1901.04560v1
fatcat:s3ezyjrlgjetzjsdg42khzbbpe
*uniform**hypergraphs*, which captures the intuitive notion*of*building a*hypergraph*piece-by-piece, and a numerical invariant called ... We show that every connected r-*uniform**hypergraph*contains a minimally connected spanning subhypergraph and provide a polynomial-time algorithm for identifying such a subhypergraph. ... Now, suppose that the result is true for all minimally connected r-*uniform**hypergraphs**of**size**k*− 1 and let H be a minimally connected r-*uniform**hypergraph**of**size**k*. ...##
###
Page 5319 of Mathematical Reviews Vol. , Issue 85m
[page]

1985
*
Mathematical Reviews
*

*K*. Dewdney, on real- izability

*of*a given sequence

*of*nonnegative integers as a degree sequence

*of*a

*uniform*

*hypergraph*, to the case

*of*an arbitrary hy- pergraph

*with*prescribed edge

*sizes*. ... In this paper the author generalizes their results for

*k*-

*uniform*

*hypergraphs*, i.e., for families

*of*

*k*-element sets. ...

##
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Analytic Connectivity in General Hypergraphs
[article]

2017
*
arXiv
*
pre-print

We prove a modified Cheeger's inequality and also give a bound on analytic connectivity

arXiv:1701.04548v1
fatcat:fkrv5tla5rgs7bw4lbdp2jbmzm
*with*respect to the degree sequence and*diameter**of*a*hypergraph*. ... In this paper we extend the known results*of*analytic connectivity to non-*uniform**hypergraphs*. ... We have obtained bounds for the analytic connectivity*of*general*hypergraphs**with*respect to*diameter*and degree sequence*of*the*hypergraph*. ...##
###
The Degree-Diameter Problem for Claw-Free Graphs and Hypergraphs

2013
*
Journal of Graph Theory
*

The

doi:10.1002/jgt.21716
fatcat:hz7d32e53vhbpetekpcizteivq
*hypergraph*Moore bound states that the order*of*a*hypergraph**of*maximum degree ∆, rank*k*and*diameter**D*is at most 1+∆*D*i=1 (∆−1) i−1 (*k*−1) i . ... For 2-regular*hypergraph**of*rank*k*≥ 3 and any*diameter**D*, we improve this bound Our construction*of*claw-free graphs*of**diameter*2 yields a similar result for*hypergraphs**of**diameter*2, degree 2 and any ... Are there similar connections between large*K*1,p -free graphs and (p − 1)-regular*hypergraphs*? Much research has been undertaken on the construction*of*large graphs*of*given degree and*diameter*. ...##
###
On the α-spectral radius of uniform hypergraphs
[article]

2018
*
arXiv
*
pre-print

For 0<α<1 and a

arXiv:1807.08112v1
fatcat:wpnlfv2cyjchdbd4lhjlxywhfm
*uniform**hypergraph*G, the α-spectral radius*of*G is the largest H-eigenvalue*of*α*D*(G) +(1-α)A(G), where*D*(G) and A(G) are the diagonal tensor*of*degrees and the adjacency tensor*of*G, respectively ... in some classes*of**uniform**hypergraphs*. ... This work was supported by the National Natural Science Foundation*of*China (No. 11071089). ...##
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On the α-spetral radius of uniform hypergraphs

2019
*
Discussiones Mathematicae Graph Theory
*

For 0 ≤ α < 1 and a

doi:10.7151/dmgt.2268
fatcat:vboodjauvrgnxdfdoxgabnubma
*uniform**hypergraph*G, the α-spectral radius*of*G is the largest H-eigenvalue*of*α*D*(G)+(1−α)A(G), where*D*(G) and A(G) are the diagonal tensor*of*degrees and the adjacency tensor*of*G ... in some classes*of**uniform**hypergraphs*. ... Acknowledgements This work was supported by the National Natural Science Foundation*of*China (No. 11671156) and the Innovation Project*of*Graduate School*of*South China Normal University. ...
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