Results 51 to 60 of about 8,142 (223)
Chromatic polynomials of hypergraphs [PDF]
, 2000 In this paper we present some hypergraphs which are chromatically characterized by their chromatic polynomials. It occurs that these hypergraphs are chromatically unique.
Borowiecki, Mieczysław, Łazuka, Ewa
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Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment
Mathematics, 2019 In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs.
Anam Luqman +2 more
doaj +1 more source
Chromatic polynomials of hypergraphs and mixed hypergraphs [PDF]
, 2020 This thesis covers two main topics: chromatic polynomials of hypergraphs and mixed ...
Zhang, Ruixue
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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
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
Annotated hypergraphs: models and applications
Applied Network Science, 2020 Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles.
Philip Chodrow, Andrew Mellor
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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
Series–parallel chromatic hypergraphs [PDF]
, 2010 In this paper two-terminal series–parallel chromatic hypergraphs are introduced and for this class of hypergraphs it is shown that the chromatic polynomial can be computed with polynomial complexity.
Bokhary, Syed Ahtsham Ul Haq +1 more
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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
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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