Here we deal with expansion properties of faulty random regular graphs and show: For fixed d⩾42 and p = κ/d, κ⩾20, a random regular graph with fault probability f = 1−p contains a linear-size subgraph which is an expander almost surely. This subgraph can be found...
random_regular_graph(d, n, seed=None) 返回$n$节点上的随机$d$-正则图。 生成的图形没有自循环或平行边。 参数 d ( int )--每个节点的度数。 n …
内容提示: Models of random regular graphsN. C. WormaldSummarygether with an exposition of some of the main methods of obtaining these results.Related results on asymptotic enumeration are also presented, as well as variousgeneralisations to random graphs with given degree sequence. A major feature...
Beside the Erdős–Rényi's G(n,p) model, another model of random graphs which also draws lots of attention is the model of random regular graphs. Let 1⩽d⩽n-1 be two positive integers, a random regular graph Gn,d is obtained by sampling uniformly at random over the set of all...
In a previous paper we showed that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6-regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a ra...
Significantlylessisknownforrandomd-regulargraphsG n,d .In[6], FriezeandLuczakextendedtheresultsof[9]forχ(G(n,p))torandom d-regulargraphs,provingthatforallintegersd>d 0 ,w.h.p.χ(G n,d )− d 2logd=Θdloglogd (logd)
bootstrap percolation on the random regular graph. random struct. algorithms 30 (1–2), 257–286 (2007) article math mathscinet google scholar bapst, v., coja-oghlan, a., hetterich, s., rassmann, f., vilenchik, d.: the condensation phase transition in random ...
Induced Subgraph in Random Regular GraphInduced subgraphPoisson distributionrandom regular graphstrictly balancedthresh-oldLet G n,d be a random d-regular graph with n vertices, where d = o(n). Given a fixed graph H, Y H denotes the number of induced copies of H in G n,d . In this ...
Random Regular Graph GenerationTo generate a random regular graph, you need to ensure that each vertex has the same degree. This is done by randomly pairing vertices and connecting them while ensuring that the degree constraint is satisfied.Algorithm...
The resulting matrix is the adjacency matrix of a random regular (multi)-graph of degree $2d$ on $n$ vertices. It is known that the distribution of smooth linear eigenvalue statistics of this matrix is given asymptotically by sums of Poisson random variables. This is in contrast with ...