منابع مشابه
Dismantling Sparse Random Graphs
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. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n→∞, then the number in question is essentially the same for all values of k that satisfy both k →∞ and k = o(n). The process of removi...
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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. Our principal observation is that, if G is a sparse random graph or a random regular graph on n vertices with n → ∞, then the number in question is essentially the same for all values of k that satisfy both k → ∞ and k = o(n). The process of rem...
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Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of ‘‘cross edges’’ between the parts. We are interested in sparse random graphs Ž . G with edge probability c n. We show that, if c ln 4, then the bisection width is n n, c n with high probability; while if c ln 4, the...
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Quasi-random graph properties form a large equivalence class of graph properties which are all shared by random graphs. In recent years, various aspects of these properties have been treated by a number of authors (e.g., see [5]-[14], [16], [23]-[27]). Almost all of these results deal with dense graphs, that is, graphs on n vertices having cn edges for some c > 0 as n → ∞. In this paper, we ext...
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We study the mixing properties of the single-site Markov chain known as the Glauber dynam-ics for sampling k-colorings of a sparse random graph G(n, d/n) for constant d. The best knownrapid mixing results for general graphs are in terms of the maximum degree ∆ of the input graphG and hold when k > 11∆/6 for all G. Improved results hold when k > α∆ for graphs withgirth ≥ 5 and ∆ ...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2008
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548307008802