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1
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Memory of Kazimierz Głazek

100%
Borowiecki M.
Discussiones Mathematicae - General Algebra and Applications
|
2005
|
tom 25
|
nr 2
141-147
2
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Chromatic polynomials of hypergraphs

64%
Borowiecki M., Łazuka E.
Discussiones Mathematicae Graph Theory
|
2000
|
tom 20
|
nr 2
293-301
EN
In this paper we present some hypergraphs which are chromatically characterized by their chromatic polynomials. It occurs that these hypergraphs are chromatically unique. Moreover we give some equalities for the chromatic polynomials of hypergraphs generalizing known results for graphs and hypergraphs of Read and Dohmen.
3
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Weakly P-saturated graphs

64%
Borowiecki M., Sidorowicz E.
Discussiones Mathematicae Graph Theory
|
2002
|
tom 22
|
nr 1
17-29
EN
For a hereditary property 𝓟 let $k_{𝓟}(G)$ denote the number of forbidden subgraphs contained in G. A graph G is said to be weakly 𝓟-saturated, if G has the property 𝓟 and there is a sequence of edges of G̅, say $e₁,e₂,...,e_l$, such that the chain of graphs $G = G₀ ⊂ G_0 + e₁ ⊂ G₁ + e₂ ⊂ ... ⊂ G_{l-1} + e_l = G_l = K_n(G_{i+1} = G_i + e_{i+1})$ has the following property: $k_{𝓟}(G_{i+1}) > k_{𝓟}(G_i)$, 0 ≤ i ≤ l-1. In this paper we shall investigate some properties of weakly saturated graphs. We will find upper bound for the minimum number of edges of weakly 𝓓ₖ-saturated graphs of order n. We shall determine the number wsat(n,𝓟) for some hereditary properties.
4
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Hamiltonicity and Generalised Total Colourings of Planar Graphs

64%
Borowiecki M., Broere I.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 2
243-257
EN
The total generalised colourings considered in this paper are colourings of graphs such that the vertices and edges of the graph which receive the same colour induce subgraphs from two prescribed hereditary graph properties while incident elements receive different colours. The associated total chromatic number is the least number of colours with which this is possible. We study such colourings for sets of planar graphs and determine, in particular, upper bounds for these chromatic numbers for proper colourings of the vertices while the monochromatic edge sets are allowed to be forests. We also prove that if an even planar triangulation has a Hamilton cycle H for which there is no cycle among the edges inside H, then such a graph needs at most four colours for a total colouring as described above. The paper is concluded with some conjectures and open problems.
5
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On partitions of hereditary properties of graphs

64%
Borowiecki M., Fiedorowicz A.
Discussiones Mathematicae Graph Theory
|
2006
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tom 26
|
nr 3
377-387
EN
In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement, in some sense, of that in Theorem is given.
6
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On Hallian digraphs and their binding number

64%
Borowiecki M., Michalak D.
Banach Center Publications
|
1989
|
tom 25
|
nr 1
33-37
7
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A characterization of middle graphs and a matroid associated with middle graphs of hypergraphs

63%
Borowiecki M.
Fundamenta Mathematicae
|
1983
|
tom 117
|
nr 1
1-4
8
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Generalized list colourings of graphs

52%
Borowiecki M., Drgas-Burchardt E., Mihók P.
Discussiones Mathematicae Graph Theory
|
1995
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tom 15
|
nr 2
185-193
EN
We prove: (1) that $ch_P(G) - χ_P(G)$ can be arbitrarily large, where $ch_P(G)$ and $χ_P(G)$ are P-choice and P-chromatic numbers, respectively, (2) the (P,L)-colouring version of Brooks' and Gallai's theorems.
9
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On generalized list colourings of graphs

52%
Borowiecki M., Broere I., Mihók P.
Discussiones Mathematicae Graph Theory
|
1997
|
tom 17
|
nr 1
127-132
EN
Vizing [15] and Erdős et al. [8] independently introduce the idea of considering list-colouring and k-choosability. In the both papers the choosability version of Brooks' theorem [4] was proved but the choosability version of Gallai's theorem [9] was proved independently by Thomassen [14] and by Kostochka et al. [11]. In [3] some extensions of these two basic theorems to (𝓟,k)-choosability have been proved. In this paper we prove some extensions of the well-known bounds for the 𝓟-chromatic number to the (𝓟,k)-choice number and then an extension of Brooks' theorem.
10
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Remarks on the existence of uniquely partitionable planar graphs

52%
Borowiecki M., Mihók P., Tuza Z., Voigt M.
Discussiones Mathematicae Graph Theory
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1999
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tom 19
|
nr 2
159-166
EN
We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (𝓓₁,𝓓₁)-partitionable planar graphs with respect to the property 𝓓₁ "to be a forest".
11
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Generalized domination, independence and irredudance in graphs

52%
Borowiecki M., Michalak D., Sidorowicz E.
Discussiones Mathematicae Graph Theory
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1997
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tom 17
|
nr 1
147-153
EN
The purpose of this paper is to present some basic properties of 𝓟-dominating, 𝓟-independent, and 𝓟-irredundant sets in graphs which generalize well-known properties of dominating, independent and irredundant sets, respectively.
12
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Acyclic reducible bounds for outerplanar graphs

52%
Borowiecki M., Fiedorowicz A., Hałuszczak M.
Discussiones Mathematicae Graph Theory
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2009
|
tom 29
|
nr 2
219-239
EN
For a given graph G and a sequence 𝓟₁, 𝓟₂,..., 𝓟ₙ of additive hereditary classes of graphs we define an acyclic (𝓟₁, 𝓟₂,...,Pₙ)-colouring of G as a partition (V₁, V₂,...,Vₙ) of the set V(G) of vertices which satisfies the following two conditions: 1. $G[V_i] ∈ 𝓟_i$ for i = 1,...,n, 2. for every pair i,j of distinct colours the subgraph induced in G by the set of edges uv such that $u ∈ V_i$ and $v ∈ V_j$ is acyclic. A class R = 𝓟₁ ⊙ 𝓟₂ ⊙ ... ⊙ 𝓟ₙ is defined as the set of the graphs having an acyclic (𝓟₁, 𝓟₂,...,Pₙ)-colouring. If 𝓟 ⊆ R, then we say that R is an acyclic reducible bound for 𝓟. In this paper we present acyclic reducible bounds for the class of outerplanar graphs.
13
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Generalized total colorings of graphs

52%
Borowiecki M., Kemnitz A., Marangio M., Mihók P.
Discussiones Mathematicae Graph Theory
|
2011
|
tom 31
|
nr 2
209-222
EN
An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P,Q)-total coloring of a simple graph G is a coloring of the vertices V(G) and edges E(G) of G such that for each color i the vertices colored by i induce a subgraph of property P, the edges colored by i induce a subgraph of property Q and incident vertices and edges obtain different colors. In this paper we present some general basic results on (P,Q)-total colorings. We determine the (P,Q)-total chromatic number of paths and cycles and, for specific properties, of complete graphs. Moreover, we prove a compactness theorem for (P,Q)-total colorings.
14
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On Hallian digraphs, permanents and transversals

51%
Arczyński M., Borowiecki M., Sysło M. M.
Colloquium Mathematicum
|
1979
|
tom 41
|
nr 1
141-145
15
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Point partition numbers and generalized Nordhaus-Gaddum problems

50%
Borowiecki M.
Colloquium Mathematicum
|
1984
|
tom 48
|
nr 2
279-285
16
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A survey of hereditary properties of graphs

46%
Borowiecki M., Broere I., Frick M., Mihók P., Semanišin G.
Discussiones Mathematicae Graph Theory
|
1997
|
tom 17
|
nr 1
5-50
EN
In this paper we survey results and open problems on the structure of additive and hereditary properties of graphs. The important role of vertex partition problems, in particular the existence of uniquely partitionable graphs and reducible properties of graphs in this structure is emphasized. Many related topics, including questions on the complexity of related problems, are investigated.
17
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Preface, Contents, Participants

38%
Skupień Z., Borowiecki M.
Banach Center Publications
|
1989
|
tom 25
|
nr 1
1-10
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