Results 31 to 40 of about 1,190 (81)

Cycles in Random Bipartite Graphs [PDF]

, 2013
In this paper we study cycles in random bipartite graph $G(n,n,p)$. We prove that if $p\gg n^{-2/3}$, then $G(n,n,p)$ a.a.s. satisfies the following. Every subgraph $G'\subset G(n,n,p)$ with more than $(1+o(1))n^2p/2$ edges contains a cycle of length $t$
Shang, Yilun
core  

Sharp thresholds for Ramsey properties

Forum of Mathematics, Sigma
In this work, we develop a unified framework for establishing sharp threshold results for various Ramsey properties. To achieve this, we view such properties as noncolourability of auxiliary hypergraphs.
Ehud Friedgut, Eden Kuperwasser, Wojciech Samotij, Mathias Schacht   +3 more
doaj   +1 more source

Zagreb connection indices on polyomino chains and random polyomino chains

Open Mathematics
In this manuscript, we delve into the exploration of the first and second Zagreb connection indices of both polyomino chains and random polyomino chains. Our methodology relies on the utilization of Markov chain theory. Within this framework, the article
Sigarreta Saylé, Cruz-Suárez Hugo
doaj   +1 more source

Extremal, enumerative and probabilistic results on ordered hypergraph matchings

Forum of Mathematics, Sigma
An ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders.
Michael Anastos, Zhihan Jin, Matthew Kwan, Benny Sudakov   +3 more
doaj   +1 more source

The rank of random regular digraphs of constant degree

, 2018
Let $d$ be a fixed large integer. For any $n$ larger than $d$, let $A_n$ be the adjacency matrix of the random directed $d$-regular graph on $n$ vertices, with the uniform distribution. We show that $A_n$ has rank at least $n-1$ with probability going to
Litvak, Alexander, Lytova, Anna, Tikhomirov, Konstantin, Tomczak-Jaegermann, Nicole, Youssef, Pierre   +4 more
core   +2 more sources

Degree-penalized contact processes

Forum of Mathematics, Sigma
In this paper we study degree-penalized contact processes on Galton-Watson (GW) trees and the configuration model. The model we consider is a modification of the usual contact process on a graph.
Zsolt Bartha, Júlia Komjáthy, Daniel Valesin   +2 more
doaj   +1 more source

Length spectrum of large genus random metric maps

Forum of Mathematics, Sigma
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach.
Simon Barazer, Alessandro Giacchetto, Mingkun Liu   +2 more
doaj   +1 more source

Distinguishing Chromatic Number of Random Cayley graphs

, 2016
The \textit{Distinguishing Chromatic Number} of a graph $G$, denoted $\chi_D(G)$, was first defined in \cite{collins} as the minimum number of colors needed to properly color $G$ such that no non-trivial automorphism $\phi$ of the graph $G$ fixes each ...
Balachandran, Niranjan, Padinhatteeri, Sajith   +1 more
core   +1 more source

Mantel's Theorem for random graphs [PDF]

, 2012
For a graph $G$, denote by $t(G)$ (resp. $b(G)$) the maximum size of a triangle-free (resp. bipartite) subgraph of $G$. Of course $t(G) \geq b(G)$ for any $G$, and a classic result of Mantel from 1907 (the first case of Tur\'an's Theorem) says that ...
DeMarco, Bobby, Kahn, Jeff
core  

Special issue on statistical analysis of networks: Preface by the guest editors. [PDF]

Stat Methods Appt, 2021
Schweinberger M, Stingo FC, Vitale MP.
europepmc   +1 more source