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Size of k-uniform hypergraph with diameter d
2003
Discrete Mathematics
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In this paper, we estimate the 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. ...
doi:10.1016/s0012-365x(02)00593-9
fatcat:7hzv7az37bblhcqjfzxcblqfcu
On the transmission of uniform unicyclic hypergraphs
[article]
2018
arXiv
pre-print
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We determine the unique 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. ...
arXiv:1808.09962v2
fatcat:5vqrv5cbrjhwfirhgxgp33jskq
Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number
2021
Discrete Dynamics in Nature and Society
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We show that balanced hyperbugs maximize the spectral radii 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 ...
doi:10.1155/2021/5805239
fatcat:qpyzeammazcavpkwgtr7wybpuu
The largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges (vertices)
[article]
2018
arXiv
pre-print
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Let S(m,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 ...
arXiv:1807.05955v2
fatcat:srgyutysknf6xef5jbudkbhv6i
The matching polynomials and spectral radii of uniform supertrees
[article]
2018
arXiv
pre-print
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Using the methods 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. ...
arXiv:1807.01180v1
fatcat:elbnrsdttjgrtnr6mogvwo2xsq
The Matching Polynomials and Spectral Radii of Uniform Supertrees
2018
Electronic Journal of Combinatorics
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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. ...
doi:10.37236/7839
fatcat:zrsnt2ogqrgmve2tmxujyy3lem
Decompositions into Subgraphs of Small Diameter
2010
Combinatorics, probability & computing
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Let P (n, , 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. ...
doi:10.1017/s0963548310000040
fatcat:pgfnioyhxzgsdfzwivqdj7357u
On the spectrum and linear programming bound for hypergraphs
[article]
2022
arXiv
pre-print
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We also determine the largest order 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. ...
arXiv:2009.03022v2
fatcat:pdteabgphnbobfe7ukambxvktq
Intersecting designs from linear programming and graphs of diameter two
1994
Discrete Mathematics
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The new results presented here are corollaries 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. ...
doi:10.1016/0012-365x(92)00478-a
fatcat:yew2albzkbhsfcwbjirbb2tctm
Minimally Connected Hypergraphs
[article]
2019
arXiv
pre-print
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In this paper, we define a construction process for minimally connected r-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. ...
arXiv:1901.04560v1
fatcat:s3ezyjrlgjetzjsdg42khzbbpe
Page 5319 of Mathematical Reviews Vol. , Issue 85m
[page]
1985
Mathematical Reviews
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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. ...
Analytic Connectivity in General Hypergraphs
[article]
2017
arXiv
pre-print
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We prove a modified Cheeger's inequality and also give a bound on analytic connectivity 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. ...
arXiv:1701.04548v1
fatcat:fkrv5tla5rgs7bw4lbdp2jbmzm
The Degree-Diameter Problem for Claw-Free Graphs and Hypergraphs
2013
Journal of Graph Theory
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The 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. ...
doi:10.1002/jgt.21716
fatcat:hz7d32e53vhbpetekpcizteivq
On the α-spectral radius of uniform hypergraphs
[article]
2018
arXiv
pre-print
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For 0<α<1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(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). ...
arXiv:1807.08112v1
fatcat:wpnlfv2cyjchdbd4lhjlxywhfm
On the α-spetral radius of uniform hypergraphs
2019
Discussiones Mathematicae Graph Theory
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For 0 ≤ α < 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(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. ...
doi:10.7151/dmgt.2268
fatcat:vboodjauvrgnxdfdoxgabnubma
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