Local Convergence and Stability of Tight Bridge-addable Classes
نویسندگان
چکیده
منابع مشابه
Local Convergence and Stability of Tight Bridge-Addable Graph Classes
A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. The authors recently proved a conjecture of McDiarmid, Steger, and Welsh stating that if G is bridge-addable and Gn is a uniform n-vertex graph from G, then Gn is connected with probability at least (1 + o(1))e−1/2. The constant e−...
متن کاملConnectivity of addable graph classes
A non-empty class A of labelled graphs is weakly addable if for each graph G ∈ A and any two distinct components of G, any graph that can be obtain by adding an edge between the two components is also in A. For a weakly addable graph class A, we consider a random element Rn chosen uniformly from the set of all graph in A on the vertex set {1, . . . , n}. McDiarmid, Steger and Welsh conjecture [...
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فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...
Connectivity of Addable Monotone Graph Classes ⋆
A class A of labelled graphs is weakly addable if if for all graphs G in A and all vertices u and v in distinct connected components of G, the graph obtained by adding an edge between u and v is also in A; the class A is monotone if for all G ∈ A and all subgraphs H of G, we have H ∈ A. We show that for any weakly addable, monotone class A whose elements have vertex set {1, . . . , n}, the prob...
متن کاملConnectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture
A class of graphs is bridge-addable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. We prove a conjecture of McDiarmid, Steger, and Welsh, that says that if Gn is any bridge-addable class of graphs on n vertices, and Gn is taken uniformly at random from Gn, then Gn is connected with probability at least e− 1 2 + o...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2018
ISSN: 0008-414X,1496-4279
DOI: 10.4153/s0008414x18000020