Results 51 to 60 of about 1,981 (215)
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 +3 more
wiley +1 more source
Embeddings and Ramsey numbers of sparse k-uniform hypergraphs [PDF]
, 2009 Chvatal, Rodl, Szemer,di and Trotter [3] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [6,23] the same result was proved for 3-uniform hypergraphs. Here we extend this result to kappa-uniform hypergraphs
Kühn, D. +9 more
core +1 more source
Recursively Constructed Uniform Hypergraphs
AlgorithmsIn this work, we introduce and study a generalization for r-uniform hypergraphs of complement-reducible graphs, the so-called co-graphs. The operations for r-join-hypergraphs are the binary disjoint union of two given r-join-hypergraphs and the r-nary ...
Frank Gurski +2 more
doaj +1 more source
A note on self-complementary hypergraphs [PDF]
Opuscula Mathematica, 2005 In the paper we describe all self-complementary hypergraphs. It turns out that such hypergraphs exist if and only if the number of vertices of the hypergraph is of the form \(n=2^k\). This answers a conjecture posed by A.
Małgorzata Zwonek
doaj
Density Conditions for k $k$ Vertex‐Disjoint Triangles in Tripartite Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Let n , k $n,k$ be positive integers such that n ≥ k $n\ge k$ and G $G$ be a tripartite graph with parts A , B , C $A,B,C$ such that ∣ A ∣ = ∣ B ∣ = ∣ C ∣ = n $| A| =| B| =| C| =n$. Denote the edge densities of G [ A , B ] , G [ A , C ] $G[A,B],G[A,C]$ and G [ B , C ] $G[B,C]$ by α , β $\alpha ,\beta $ and γ $\gamma $, respectively.
Mingyang Guo, Klas Markström
wiley +1 more source
A lifting of graphs to 3-uniform hypergraphs, its generalization, and further investigation of hypergraph Ramsey numbers [PDF]
, 2015 Ramsey theory has posed many interesting questions for graph theorists that have yet to besolved. Many different methods have been used to find Ramsey numbers, though very feware actually known.
NC DOCKS at Western Carolina University +1 more
core
Chromatic Ramsey Numbers and Two‐Color Turán Densities
Journal of Graph Theory, EarlyView.ABSTRACT Given a graph G, its 2‐color Turán number ex ( 2 ) ( n , G ) is the maximum number of edges in an n‐vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of G. Let π ( 2 ) ( G ) = lim n → ∞ ex ( 2 ) ( n , G ) / n 2 be the 2‐color Turán density of G.
Maria Axenovich, Simon Gaa, Dingyuan Liu
wiley +1 more source
Discrete Mathematics, 1986 \textit{D. Buset} [Discrete Math. 57, 297-299 (1985; Zbl 0587.05030)] determined for \(k=2\) the sets of all pairs (a,b) such that there exists a k-uniform (connected k-uniform) hypergraph whose automorphism group has exactly a orbits on the set of vertices and b orbits on the set of edges. The author extended this result for arbitrary natural k.
openaire +2 more sources
The Uniformity Space of Hypergraphs [PDF]
, 2012 For a hypergraph H=(V,E) and a field F, a weighting of H is a map f:V ?F. A weighting is called stable if there is some k ? F such that the sum of the weights on each edge of H is equal to k.
Mol, Lucas
core
Extremal problems in 3-uniform hypergraphs [PDF]
, 2021 In this thesis we proved three results for 3-uniform dense hypergraphs. In each case, we determined conditions for the existence of different kinds of substructures.
Piga, Simón
core