Results 11 to 20 of about 1,157 (63)
Limit distribution of degrees in random family trees [PDF]
, 2010 In a one-parameter model for evolution of random trees, which also includes the Barabasi-Albert random tree, almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. Results about Polya urn models are
Backhausz, Agnes
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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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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
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Lower bounds for bootstrap percolation on Galton-Watson trees [PDF]
, 2014 Bootstrap percolation is a cellular automaton modelling the spread of an `infection' on a graph. In this note, we prove a family of lower bounds on the critical probability for $r$-neighbour bootstrap percolation on Galton--Watson trees in terms of ...
Gunderson, Karen, Przykucki, Michał
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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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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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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
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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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, 2014 Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs.
Deák, Attila
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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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