Filters








1,060 Hits in 4.7 sec

Size of k-uniform hypergraph with diameter d

Miaolin Ye
2003 Discrete Mathematics  
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]

Hongying Lin, Bo Zhou
2018 arXiv   pre-print
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

Qiannan Niu, Haizhen Ren, Lei Zhang, Akbar Ali
2021 Discrete Dynamics in Nature and Society  
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]

Cunxiang Duan, Ligong Wang, Peng Xiao
2018 arXiv   pre-print
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]

Li Su, Liying Kang, Honghai Li, Erfang Shan
2018 arXiv   pre-print
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

Li Su, Liying Kang, Honghai Li, Erfang Shan
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.  ... 
doi:10.37236/7839 fatcat:zrsnt2ogqrgmve2tmxujyy3lem

Decompositions into Subgraphs of Small Diameter

JACOB FOX, BENNY SUDAKOV
2010 Combinatorics, probability & computing  
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]

Sebastian M. Cioabă, Jack H. Koolen, Masato Mimura, Hiroshi Nozaki, Takayuki Okuda
2022 arXiv   pre-print
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

Zoltán Füredi
1994 Discrete Mathematics  
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]

Mark Budden, Josh Hiller, Andrew Penland
2019 arXiv   pre-print
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  
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]

Ashwin Guha, Muni Sreenivas Pydi, Biswajit Paria, Ambedkar Dukkipati
2017 arXiv   pre-print
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

Peter Dankelmann, Tomáš Vetrík
2013 Journal of Graph Theory  
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]

HaiYan Guo, Bo Zhou
2018 arXiv   pre-print
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

Haiyan Guo, Bo Zhou
2019 Discussiones Mathematicae Graph Theory  
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
« Previous Showing results 1 — 15 out of 1,060 results