Results 21 to 30 of about 1,132 (55)
High-Precision Entropy Values for Spanning Trees in Lattices
, 2003 Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the ...
Ball K +11 more
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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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Dismantling sparse random graphs
, 2007 We consider the number of vertices that must be removed from a graph G in order that the remaining subgraph has no component with more than k vertices.
Janson, Svante, Thomason, Andrew
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INVARIANT MEASURES CONCENTRATED ON COUNTABLE STRUCTURES
Forum of Mathematics, Sigma, 2016 Let $L$ be a countable language. We say that a countable infinite $L$
NATHANAEL ACKERMAN +2 more
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Two-Point Concentration of the Independence Number of the Random Graph
Forum of Mathematics, SigmaWe show that the independence number of $ G_{n,p}$ is concentrated on two values if $ n^{-2/3+ \epsilon } < p \le 1$ . This result is roughly best possible as an argument of Sah and Sawhney shows that the independence number is not, in ...
Tom Bohman, Jakob Hofstad
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Local Large deviation: A McMillian Theorem for Coloured Random Graph Processes
, 2017 For a finite typed graph on $n$ nodes and with type law $\mu,$ we define the so-called spectral potential $\rho_{\lambda}(\,\cdot,\,\mu),$ of the graph.From the $\rho_{\lambda}(\,\cdot,\,\mu)$ we obtain Kullback action or the deviation function ...
Doku-Amponsah, Kwabena
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The $(k,\ell)$-rainbow index of random graphs [PDF]
, 2013 A tree in an edge colored graph is said to be a rainbow tree if no two edges on the tree share the same color. Given two positive integers $k$, $\ell$ with $k\geq 3$, the \emph{$(k,\ell)$-rainbow index} $rx_{k,\ell}(G)$ of $G$ is the minimum number of ...
Cai, Qingqiong +2 more
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Zagreb connection indices on polyomino chains and random polyomino chains
Open MathematicsIn 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
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The Incipient Giant Component in Bond Percolation on General Finite Weighted Graphs
, 2016 On a large finite connected graph let edges $e$ become "open" at independent random Exponential times of arbitrary rates $w_e$. Under minimal assumptions, the time at which a giant component starts to emerge is weakly concentrated around its ...
Aldous, David J.
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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
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