Results 11 to 20 of about 1,132 (55)
Queues, random graphs and branching processes
International Journal of Stochastic Analysis, Volume 1, Issue 3, Page 223-243, 1988., 1988 In this paper it is shown that certain basic results of queueing theory can be used successfully in solving various problems of random graphs and branching processes.
Lajos Takács
wiley +1 more source
Upper tails for triangles [PDF]
, 2010 With $\xi$ the number of triangles in the usual (Erd\H{o}s-R\'enyi) random graph $G(m,p)$, $p>1/m$ and $\eta>0$, we show (for some $C_{\eta}>0$) $$\Pr(\xi> (1+\eta)\E \xi) < \exp[-C_{\eta}\min{m^2p^2\log(1/p),m^3p^3}].$$ This is tight up to the value of $
Alon +10 more
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Limit theorems for the weights and the degrees in anN-interactions random graph model
Open Mathematics, 2016 A random graph evolution based on interactions of N vertices is studied. During the evolution both the preferential attachment rule and the uniform choice of vertices are allowed. The weight of an M-clique means the number of its interactions.
Fazekas István, Porvázsnyik Bettina
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SYMMETRIC AND ASYMMETRIC RAMSEY PROPERTIES IN RANDOM HYPERGRAPHS
Forum of Mathematics, Sigma, 2017 A celebrated result of Rödl and Ruciński states that for every graph $F$ , which is not a forest of stars and paths of length 3, and fixed number of colours
LUCA GUGELMANN +5 more
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Ramsey Properties of Random Graphs and Folkman Numbers
Discussiones Mathematicae Graph Theory, 2017 For two graphs, G and F, and an integer r ≥ 2 we write G → (F)r if every r-coloring of the edges of G results in a monochromatic copy of F. In 1995, the first two authors established a threshold edge probability for the Ramsey property G(n, p) → (F)r ...
Rödl Vojtěch +2 more
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Symmetric motifs in random geometric graphs [PDF]
, 2017 We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency spectrum as sharp,
Dettmann, Carl P., Knight, Georgie
core +3 more sources
The Largest Component in Critical Random Intersection Graphs
Discussiones Mathematicae Graph Theory, 2018 In this paper, through the coupling and martingale method, we prove the order of the largest component in some critical random intersection graphs is n23$n^{{2 \over 3}}$ with high probability and the width of scaling window around the critical ...
Wang Bin, Wang Longmin, Xiang Kainan
doaj +1 more source
TRANSFERENCE FOR THE ERDŐS–KO–RADO THEOREM
Forum of Mathematics, Sigma, 2015 For natural numbers $n,r\in \mathbb{N}$ with $n\geqslant r$, the Kneser graph $K(n,r)$ is the graph on the family of $r$-element subsets of $\{1,\ldots ,n\}$ in which two sets are adjacent if and only if they are disjoint.
JÓZSEF BALOGH +2 more
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The skew energy of random oriented graphs [PDF]
, 2013 Given a graph $G$, let $G^\sigma$ be an oriented graph of $G$ with the orientation $\sigma$ and skew-adjacency matrix $S(G^\sigma)$. The skew energy of the oriented graph $G^\sigma$, denoted by $\mathcal{E}_S(G^\sigma)$, is defined as the sum of the ...
Chen, Xiaolin +2 more
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EIGENVALUES AND LINEAR QUASIRANDOM HYPERGRAPHS
Forum of Mathematics, Sigma, 2015 Let $p(k)$ denote the partition function of $k$. For each $k\geqslant 2$, we describe a list of $p(k)-1$ quasirandom properties that a $k$-uniform hypergraph can have. Our work connects previous notions on linear hypergraph quasirandomness by Kohayakawa,
JOHN LENZ, DHRUV MUBAYI
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