Problems from the world surrounding perfect graphs
A. Gyárfás (1987)
Applicationes Mathematicae
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A. Gyárfás (1987)
Applicationes Mathematicae
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Ivan Gutman (1989)
Publications de l'Institut Mathématique
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Van Bang Le (2000)
Discussiones Mathematicae Graph Theory
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Magda Dettlaff, Magdalena Lemańska, Gabriel Semanišin, Rita Zuazua (2016)
Discussiones Mathematicae Graph Theory
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We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k ≥ 2. Moreover, we provide a complete characterisation of (ψ2 − γ1)- perfect graphs describing the set of its forbidden induced subgraphs and providing the explicit characterisation of the structure...
Tomislav Doslić (2005)
Discussiones Mathematicae Graph Theory
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It is shown in this note that some matching-related properties of graphs, such as their factor-criticality, regularizability and the existence of perfect 2-matchings, are preserved when iterating Mycielski's construction.
Igor E. Zverovich (2006)
Discussiones Mathematicae Graph Theory
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We solve Open Problem (xvi) from Perfect Problems of Chvátal [1] available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex: Is there a class C of perfect graphs such that (a) C does not include all perfect graphs and (b) every perfect graph contains a vertex whose neighbors induce a subgraph that belongs to C? A class P is called locally reducible if there exists a proper subclass C of P such that every graph in P contains a local subgraph...
Arie M. C. A. Koster, Annegret K. Wagler (2008)
RAIRO - Operations Research - Recherche Opérationnelle
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Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs where the stable set polytope coincides with the fractional stable set polytope . For all imperfect graphs it holds that . It is, therefore, natural to use the difference between the two polytopes in order to decide how far an imperfect graph is away from being perfect. We discuss...
Eugen Mândrescu (1991)
Czechoslovak Mathematical Journal
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Alina Szelecka, Andrzej Włoch (1996)
Discussiones Mathematicae Graph Theory
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Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra andD. Basavayya [5]. In this paper we discuss strong perfectness and co-strong perfectness for the generalized composition (the lexicographic...
Barik, S., Nath, M., Pati, S., Sarma, B.K. (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Marta Borowiecka-Olszewska, Ewa Drgas-Burchardt (2017)
Discussiones Mathematicae Graph Theory
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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...
I. Gutman (1980)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Odile Favaron (1996)
Discussiones Mathematicae Graph Theory
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A graph is said to be k-factor-critical if the removal of any set of k vertices results in a graph with a perfect matching. We study some properties of k-factor-critical graphs and show that many results on q-extendable graphs can be improved using this concept.