Results 41 to 50 of about 653 (189)

Degree and Regularity of Eulerian Ideals of Hypergraphs

The Electronic Journal of Combinatorics, 2022
We define the Eulerian ideal of a $k$-uniform hypergraph and study its degree and Castelnuovo-Mumford regularity. The main tool is a Gröbner basis of the ideal obtained combinatorially from the hypergraph. We define the notion of parity join in a hypergraph and show that the regularity of the Eulerian ideal is equal to the maximum cardinality of such a
Jorge Neves, Gonçalo Varejão
openaire   +3 more sources

A Perfect Sampler for Hypergraph Independent Sets [PDF]

, 2022
The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a similar condition of the asymmetric Lovász local lemma.
Qiu, Guoliang, Wang, Yanheng, Zhang, Chihao   +2 more
core   +1 more source

3D-Via Driven Partitioning for 3D VLSI Integrated Circuits

CLEI Electronic Journal, 2010
A 3D circuit is the stacking of regular 2D circuits. The advances on the fabrication and packaging technologies allowed interconnecting stacked 2D circuits by using 3D vias.
Sandro Sawicki, Gustavo Wilke, Marcelo Johann, Ricardo Reis   +3 more
doaj   +1 more source

Topology‐Aware Deep Learning on Higher‐Order Structures for Drug Response Prediction

Advanced Science, EarlyView.
We present TopDr, a topology‐aware deep learning framework that encodes both drugs and cell lines as multiscale simplicial complexes, capturing interactions at the 0‐, 1‐, and 2‐simplex levels. By jointly integrating local higher‐order neighborhoods and global topological structures, TopDr generates enriched representations for sensitivity prediction ...
Cong Shen, Guancen Lin, Chuan‐Shen Hu, Yong Wang   +3 more
wiley   +1 more source

Explicit Construction of the (13, 13)-Regular Hypergraph

, 2010
In this article we calculate explicitly the Ramanujan (13, 13)-regular hypergraph introduced in [Sarveniazi 07] using the computer algebra programs MAGMA and OCTAVE.
Sarveniazi, Alireza, Stefan Wiedmann, Wiedmann, Stefan, Alireza Sarveniazi   +3 more
core   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Conflict-free hypergraph matchings

, 2022
A celebrated theorem of Pippenger, and Frankl and R & ouml;dl states that every almost-regular, uniform hypergraph H$\mathcal {H}$ with small maximum codegree has an almost-perfect matching. We extend this result by obtaining a conflict-free matching,
Joos, Felix, Glock, Stefan, Kim, Jaehoon, Kühn, Marcus, Lichev, Lyuben   +4 more
core   +2 more sources

On Tight Tree‐Complete Hypergraph Ramsey Numbers

Journal of Graph Theory, EarlyView.
ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley   +1 more source

Orientations of Graphs With at Most One Directed Path Between Every Pair of Vertices

Journal of Graph Theory, EarlyView.
ABSTRACT Given a graph G $G$, we say that an orientation D $D$ of G $G$ is a KT orientation if, for all u , v ∈ V ( D ) $u,v\in V(D)$, there is at most one directed path (in any direction) between u $u$ and v $v$. Graphs that admit such orientations have been used to construct graphs with large chromatic number and small clique number that served as ...
Barbora Dohnalová, Jiří Kalvoda, Gaurav Kucheriya, Sophie Spirkl   +3 more
wiley   +1 more source

Quantum walks on regular uniform hypergraphs [PDF]

Scientific Reports, 2018
AbstractQuantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information stored inherently. Therefore, we can explore the potential of quantum walks on hypergraphs.
Ying Liu, Jiabin Yuan, Bojia Duan, Dan Li   +3 more
openaire   +3 more sources