Results 61 to 70 of about 21,746 (178)

Bipartite Ramsey numbers of large cycles

, 2018
For an integer $r\geq 2$ and bipartite graphs $H_i$, where $1\leq i\leq r$, the bipartite Ramsey number $br(H_1,H_2,\ldots,H_r)$ is the minimum integer $N$ such that any $r$-edge coloring of the complete bipartite graph $K_{N,N}$ contains a monochromatic subgraph isomorphic to $H_i$ in color $i$ for some $i$, $1\leq i\leq r$.
Liu, Shaoqiang, Peng, Yuejian
openaire   +2 more sources

Upper Bounds for Linear Graph Codes

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT A linear graph code is a family 𝒞 of graphs on n$$ n $$ vertices with the property that the symmetric difference of the edge sets of any two graphs in 𝒞 is also the edge set of a graph in 𝒞. In this article, we investigate the maximal size of a linear graph code that does not contain a copy of a fixed graph H$$ H $$.
Leo Versteegen
wiley   +1 more source

Immersions of Directed Graphs in Tournaments

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT Recently, Draganić, Munhá Correia, Sudakov and Yuster (2022) showed that every tournament on (2+o(1))k2$$ \left(2+o(1)\right){k}^2 $$ vertices contains a 1‐subdivision of a transitive tournament on k$$ k $$ vertices, which is tight up to a constant factor. We prove a counterpart of their result for immersions.
António Girão, Robert Hancock
wiley   +1 more source

Typical Structure of Hereditary Graph Families. I. Apex‐free Families

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT A family of graphs ℱ$$ \mathcal{F} $$ is hereditary if ℱ$$ \mathcal{F} $$ is closed under isomorphism and taking induced subgraphs. The speed of ℱ$$ \mathcal{F} $$ is the sequence {|ℱn|}n∈ℕ$$ {\left\{|{\mathcal{F}}^n|\right\}}_{n\in \mathbb{N}} $$, where ℱn$$ {\mathcal{F}}^n $$ denotes the set of graphs in ℱ$$ \mathcal{F} $$ with the vertex ...
Sergey Norin, Yelena Yuditsky
wiley   +1 more source

Off‐Diagonal Ramsey Numbers for Slowly Growing Hypergraphs

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT For a k‐uniform hypergraph F$$ F $$ and a positive integer n$$ n $$, the Ramsey number r(F,n)$$ r\left(F,n\right) $$ denotes the minimum N$$ N $$ such that every N$$ N $$‐vertex F$$ F $$‐free k$$ k $$‐uniform hypergraph contains an independent set of n$$ n $$ vertices.
Sam Mattheus, Dhruv Mubayi, Jiaxi Nie, Jacques Verstraëte   +3 more
wiley   +1 more source

Entanglement swapping using hyperentangled pairs of two‐level neutral atoms

IET Quantum Communication, Volume 6, Issue 1, January/December 2025.
Hyperentangled swapping is a quantum communication technique that involves the exchange of hyperentangled states, which are quantum states entangled in multiple degrees of freedom, to enable secure and efficient quantum information transfer. In this paper, we demonstrate schematics for the hyperentanglement swapping between separate pairs of neutral ...
Syed Sajal Hasan, Syed Muhammad Arslan Anis, Muhammad Imran, Rameez‐ul Islam, Saif Al‐Kuwari, Tasawar Abbas   +5 more
wiley   +1 more source

Density theorems for bipartite graphs and related Ramsey-type results

, 2007
In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density.
Fox, Jacob, Sudakov, Benny
core   +4 more sources

Embedding large subgraphs into dense graphs

, 2009
What conditions ensure that a graph G contains some given spanning subgraph H? The most famous examples of results of this kind are probably Dirac's theorem on Hamilton cycles and Tutte's theorem on perfect matchings. Perfect matchings are generalized by
Kühn, Daniela, Osthus, Deryk
core   +1 more source

A sharp threshold for random graphs with a monochromatic triangle in every edge coloring

, 2003
Let $\R$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper we establish a sharp threshold for random graphs with this property.
Friedgut, Ehud, Rodl, Vojtech, Rucinski, Andrzej, Tetali, Prasad   +3 more
core   +3 more sources