Carathéodory’s Theorem and moduli of local connectivity

A Brooks Type Theorem for the Maximum Local Edge Connectivity

For a graph G, let χ(G) and λ(G) denote the chromatic number of G and the maximum local edge connectivity of G, respectively. A result of Dirac implies that every graph G satisfies χ(G) 6 λ(G) + 1. In this paper we characterize the graphs G for which χ(G) = λ(G) + 1. The case λ(G) = 3 was already solved by Aboulker, Brettell, Havet, Marx, and Trotignon. We show that a graph G with λ(G) = k > 4 ...

ساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings

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...

The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. However the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. Nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by Blaise Pascal and Pierre de Fer...

Local connectivity of the

Connectivity of local tournaments

For a local tournament D with minimum out-degree δ, minimum indegree δ− and irregularity ig(D), we give a lower bound on the connectivity of D, namely κ(D) ≥ (2 ·max{δ+, δ−}+ 1− ig(D))/3 if there exists a minimum separating set S such that D − S i is a tournament, and κ(D) ≥ (2 ·max{δ+, δ−}+ 2|δ+ − δ−|+ 1− 2ig(D))/3 otherwise. This generalizes a result on tournaments presented by C. Thomassen [...