Papers by Ewa Drgas-Burchardt
Ars Mathematica Contemporanea, 2021
Let f be a function which assigns list sizes to the vertices of G. A graph G is said to be (f,P)−... more Let f be a function which assigns list sizes to the vertices of G. A graph G is said to be (f,P)−choosable if for every collection of lists L whose sizes are specified by f a graph G is P − choosable with L. The P − sum choice number is the minimum of the sum of sizes in f over all f such that G is (f,P)− choosable. Using the notions defined above, we present some general results connected to arbitrary induced hereditary class P. We pay special attention to the class P of acyclic graphs with particular emphasis on bipartite graphs.
Results in Mathematics, 2021
We consider arc colourings of oriented graphs such that for each vertex the colours of all out-ar... more 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 tournaments, oriented graphs with small maximum degree, oriented graphs with small order and some other classes of oriented graphs. We state the conjecture that for each graph there exists a consecutive colourable orientation and confirm the conjecture for complete graphs, 2-degenerate graphs, planar graphs with girth at least 8, and bipartite graphs with arboricity at most two that include all planar bipartite graphs. Additionally, we prove that the conjecture is true for all perfect consecutively colourable graphs and for all forbidden graphs for the class of perfect consecutively colourable graphs.
Discussiones Mathematicae Graph Theory, 2018
Discussiones Mathematicae Graph Theory, 2020
Discussiones Mathematicae Graph Theory, 2020
Discussiones Mathematicae Graph Theory, 2017
Discrete Applied Mathematics, 2016
European Journal of Combinatorics, 2011
v n }, E) replacing every vertex v i of H by the graph G i and joining the vertices of G i with a... more v n }, E) replacing every vertex v i of H by the graph G i and joining the vertices of G i with all the vertices of those of G j whenever {v i , v j } ∈ E(H). For unlabelled graphs G 1 ,. .. , G n , H, let ϕ H (G 1 ,. .. , G n) stand for the class of all graphs H[G 1 ,. .. , G n ] taken over all possible orderings of V (H). A prime inductive class of graphs, I(B, C), is said to be a set of all graphs, which can be produced by recursive applying of ϕ H (G 1 ,. .. , G |V (H)|) where H is a graph from a fixed set C of prime graphs and G 1 ,. .. , G |V (H)| are either graphs from the set B of prime graphs or graphs obtained in the previous steps. Similar inductive definitions for cographs, k-trees, series-parallel graphs, Halin graphs, bipartite cubic graphs or forbidden structures of some graph classes were considered in the literature (Batagelj (1994) [1] Drgas-Burchardt et al. (2010) [6] and Hajós (1961) [10]). This paper initiates a study of prime inductive classes of graphs giving a result, which characterizes, in their language, the substitution closed induced hereditary graph classes. Moreover, for an arbitrary induced hereditary graph class P it presents a method for the construction of maximal induced hereditary graph classes contained in P and substitution closed. The main contribution of this paper is to give a minimal forbidden graph characterization of induced hereditary prime inductive classes of graphs. As a consequence, the minimal forbidden graph characterization for some special induced hereditary prime inductive graph classes is given There is also offered an algebraic view on the class of all prime inductive classes of graphs of the type I({K 1 }, C).
Electronic Notes in Discrete Mathematics, 2006
Discussiones Mathematicae Graph Theory, 2009
Discussiones Mathematicae Graph Theory, 2005
The hereditary property of hypergraphs generated by the cost colouring notion is considered in th... more 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.
Discussiones Mathematicae Graph Theory, 2006
Discussiones Mathematicae Graph Theory, 2013
Discrete Mathematics, 2012
Discrete Mathematics, 1993
Discrete Mathematics, 2004
Discrete Mathematics, 1993
ABSTRACT We prove the chromatic uniqueness of some families of graphs by using a special function... more ABSTRACT We prove the chromatic uniqueness of some families of graphs by using a special function which is the difference between the size of the line graph and the number of triangles of a given graph. Moreover, this function can be helpful in finding graphs chromatically equivalent to a given graph. We give a few examples showing how to generate such classes of graphs by using this function.
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Papers by Ewa Drgas-Burchardt