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.
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.
We introduce a 2-factor approximation algorithm for the minimum total covering number problem.
In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.
Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.