Results 41 to 50 of about 418 (155)
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
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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 +3 more
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Counting independent sets in regular hypergraphs
Journal of Combinatorial Theory, Series A, 2021 4 pages ...
József Balogh +2 more
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Sparse Graphs With Local Covering Conditions on Edges
Journal of Graph Theory, EarlyView.ABSTRACT In 1988, Erdős suggested the question of minimizing the number of edges in a connected n $n$‐vertex graph where every edge is contained in a triangle. Shortly after, Catlin, Grossman, Hobbs, and Lai resolved this in a stronger form. In this paper, we study a natural generalization of the question of Erdős in which we replace “triangle” with ...
Debsoumya Chakraborti +3 more
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Indecomposable regular graphs and hypergraphs
Discrete Mathematics, 1992 A hypergraph \(H\) consists of a finite nonempty set \(V(H)\) called the vertex set and a collection \(E(H)\) (called the edge set of \(H)\) of subsets of the power set of \(V(H)\). Note \(E(H)\) may contain the same set more then once. The number of times an element \(e\) in \(E(H)\) appears in \(E(H)\) is called its multiplicity denoted by \(m_ H(e)\)
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On Almost-Regular Edge Colourings of Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2016 We prove that if ${\cal{H}}=(V({\cal{H}}),{\cal{E}}({\cal{H}}))$ is a hypergraph, $\gamma$ is an edge colouring of ${\cal{H}}$, and $S\subseteq V({\cal{H}})$ such that any permutation of $S$ is an automorphism of ${\cal{H}}$, then there exists a permutation $\pi$ of ${\cal{E}}({\cal{H}})$ such that $|\pi(E)|=|E|$ and $\pi(E)\setminus S=E\setminus S ...
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Saturated Partial Embeddings of Planar Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph G $G$, we say that a plane subgraph H ⊆ G $H\subseteq G$ is a plane‐saturated subgraph if adding any edge (possibly with new vertices) to H $H$ would either violate planarity or make the resulting graph no longer a subgraph of
Alexander Clifton, Nika Salia
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Hypergraphs, Quasi-randomness, and Conditions for Regularity
Journal of Combinatorial Theory, Series A, 2002 The study of quasi-randomness is a flourishing topic on uniform hypergraphs. F. R. K. Chung and R. L. Graham (among others) investigated thoroughly quasi-random uniform hypergraphs of density 1/2, showing a series of important equivalent statements about these structures. In this investigations the notion of deviation plays a central role.
Yoshiharu Kohayakawa +2 more
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Knee Surgery, Sports Traumatology, Arthroscopy, EarlyView.Abstract Purpose To systematically evaluate the performance, methodological quality, and translational barriers of deep learning (DL) models for predicting knee osteoarthritis (KOA) progression from medical imaging. Methods Following PRISMA guidelines, we searched PubMed, Scopus, and Web of Science (inception to June 2026) for peer‐reviewed studies ...
Amna Gillani +5 more
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Matchings in hypergraphs and Castelnuovo--Mumford regularity [PDF]
Publicationes Mathematicae Debrecen, 2017 In this paper, we introduce and generalize some combinatorial invariants of graphs such as matching number and induced matching number to hypergraphs. Then we compare them together and present some upper bounds for the regularity of Stanley-Reisner ring of $Δ_{\mathcal{H}}$ for certain hypergraphs $\mathcal{H}$ in terms of the introduced matching ...
Khosh-Ahang, Fahimeh, Moradi, Somayeh
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