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An anti-Ramsey theorem on edge-cuts

Juan José Montellano-Ballesteros (2006)

Discussiones Mathematicae Graph Theory

Let G = (V(G), E(G)) be a connected multigraph and let h(G) be the minimum integer k such that for every edge-colouring of G, using exactly k colours, there is at least one edge-cut of G all of whose edges receive different colours. In this note it is proved that if G has at least 2 vertices and has no bridges, then h(G) = |E(G)| -|V(G)| + 2.

An application of nonprarametric Cox regression model in reliability analysis: a case study

Petr Volf (2004)

Kybernetika

The contribution deals with an application of the nonparametric version of Cox regression model to the analysis and modeling of the failure rate of technical devices. The objective is to recall the method of statistical analysis of such a model, to adapt it to the real–case study, and in such a way to demonstrate the flexibility of the Cox model. The goodness-of-fit of the model is tested, too, with the aid of the graphical test procedure based on generalized residuals.

An application of Pólya’s enumeration theorem to partitions of subsets of positive integers

Xiao Jun Wu, Chong-Yun Chao (2005)

Czechoslovak Mathematical Journal

Let S be a non-empty subset of positive integers. A partition of a positive integer n into S is a finite nondecreasing sequence of positive integers a 1 , a 2 , ⋯ , a r in S with repetitions allowed such that ∑ i = 1 r a i = n . Here we apply Pólya’s enumeration theorem to find the number ( n ; S ) of partitions of n into S , and the number D P ( n ; S ) of distinct partitions of n into S . We also present recursive formulas for computing ( n ; S ) and D P ( n ; S ) .

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