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1
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A Note on the Uniqueness of Stable Marriage Matching

100%
Drgas-Burchardt E.
Discussiones Mathematicae Graph Theory
|
2013
|
tom 33
|
nr 1
49-55
EN
In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.
2
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Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties

100%
Drgas-Burchardt E.
Discussiones Mathematicae Graph Theory
|
2009
|
tom 29
|
nr 2
263-274
EN
An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let $L^a$ denote a class of all such properties. In the paper, we consider H-reducible over $L^a$ properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.
3
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A note on joins of additive hereditary graph properties

100%
Drgas-Burchardt E.
Discussiones Mathematicae Graph Theory
|
2006
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tom 26
|
nr 3
413-418
EN
Let $L^a$ denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set $(L^a, ⊆ )$ is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in $(L^a, ⊆ )$ has a finite or infinite family of minimal forbidden subgraphs.
4
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Forbidden Structures for Planar Perfect Consecutively Colourable Graphs

64%
Borowiecka-Olszewska M., Drgas-Burchardt E.
Discussiones Mathematicae Graph Theory
|
2017
|
tom 37
|
nr 2
315-336
EN
A consecutive colouring of a graph is a proper edge colouring with posi- tive 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. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.
5
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Maximal hypergraphs with respect to the bounded cost hereditary property

64%
Drgas-Burchardt E., Fiedorowicz A.
Discussiones Mathematicae Graph Theory
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2005
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tom 25
|
nr 1-2
67-77
EN
The hereditary property of hypergraphs generated by the cost colouring notion is considered in the paper. First, we characterize all maximal graphs with respect to this property. Second, we give the generating function for the sequence describing the number of such graphs with the numbered order. Finally, we construct a maximal hypergraph for each admissible number of vertices showing some density property. All results can be applied to the problem of information storage.
6
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Generalized list colourings of graphs

51%
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.
7
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Preface

51%
Drgas-Burchardt E., Sidorowicz E.
Discussiones Mathematicae Graph Theory
|
2015
|
tom 35
|
nr 2
313-314
8
Content available remote

Preface

51%
Drgas-Burchardt E., Sidorowicz E.
Discussiones Mathematicae Graph Theory
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2017
|
tom 37
|
nr 2
299-300
9
Content available remote

Preface

45%
Drgas-Burchardt E., Hałuszczak M., Kwaśnik M., Michalak D., Sidorowicz E.
Discussiones Mathematicae Graph Theory
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2013
|
tom 33
|
nr 1
5-6
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