Marta Borowiecka-Olszewska

Marta Borowiecka-Olszewska
University of Zielona Góra | UZ · Division of Discrete Mathematics and Computer Science

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14
Publications
516
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43
Citations
Citations since 2016
5 Research Items
29 Citations
201620172018201920202021202201234567
201620172018201920202021202201234567
201620172018201920202021202201234567
201620172018201920202021202201234567

Publications

Publications (14)
Article
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Kingman, in his seminal work [13], introduced a new type of convolution of distributions that is naturally related to spherically symmetric random walks. Motivated by this paper, Urbanik in a series of papers [17] established a theory of generalized convolutions ⋄ as certain binary commutative and associative operations that include classical and K...
Article
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We consider arc colourings of oriented graphs such that for each vertex the colours of all out-arcs incident with the vertex and the colours of all in-arcs incident with the vertex form intervals. We prove that the existence of such a colouring is an NP-complete problem. We give the solution of the problem for r -regular oriented graphs, transitive...
Article
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A consecutive colouring of a graph is a proper edge colouring with positive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevastjanov showed that the corresponding decision problem is N P-...
Article
A proper edge colouring of a graph with natural numbers is consecutive if colours of edges incident with each vertex form an interval of integers. The deficiency of a graph is the minimum number of pendant edges whose attachment to makes it consecutively colourable. In 1999 Giaro, Kubale and Małafiejski considered the deficiency of the Hertz graphs...
Article
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In this paper, we present a comprehensive theory of generalized and weak generalized convolutions, illustrate it by a large number of examples, and discuss the related infinitely divisible distributions. We consider L\'evy and additive process with respect to generalized and weak generalized convolutions as certain Markov processes, and then study...
Article
Let F be a graph and let G, H denote nonempty families of graphs. We write F → (G,H) if in any 2-colouring of edges of F with red and blue, there is a red subgraph isomorphic to some graph from G or a blue subgraph isomorphic to some graph from H. The graph F without isolated vertices is said to be a (G,H)-minimal graph if F → (G,H) and F -e/→ (G,H...
Article
Aproper edge colouring of agraph with natural numbers is consecutive if colours of edges incident with each vertex form aconsecutive interval of integers. Thedeficiency def(G) of agraph G is theminimum number of pendant edges whose attachment to G makes it consecutively colourable. Since all 1-trees are consecutively colourable, in this paper we st...
Article
Let P be a property of graphs. A graph G is vertex (P,k)-colourable if the vertex set V(G) of G can be partitioned into k sets V1,V2,…,Vk such that the subgraph G[Vi] of G belongs to P, i=1,2,…,k. If P is a hereditary property, then the set of minimal forbidden subgraphs of P is defined as follows: F(P)={G:G∉PbuteachpropersubgraphHofGbelongstoP}. I...
Article
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In this paper we consider a symmetric α-stable p-sub-stable two-dimensional random vectors. Our purpose is show when the function exp { − (|a| p + |b| p) α/p } is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based...
Article
Full-text available
In this paper we consider random sum Θ i=1 X i of independent, identically distributed random variables X1, X2,. .. , with random variable Θ having geometric distribution with parameter p, independent of all X i 's. The question is to characterize such random variables X for which the distribution of this sum is the same as distribution of rescaled...

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