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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Andrzej Włoch (1999)
Discussiones Mathematicae Graph Theory
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In this paper, we propose a generalization of well known kinds of perfectness of graphs in terms of distances between vertices. We introduce generalizations of α-perfect, χ-perfect, strongly perfect graphs and we establish the relations between them. Moreover, we give sufficient conditions for graphs to be perfect in generalized sense. Other generalizations of perfectness are given in papers [3] and [7].
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...
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...
I. Gutman (1980)
Publications de l'Institut Mathématique [Elektronische Ressource]
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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...
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...
Barik, S., Nath, M., Pati, S., Sarma, B.K. (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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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.
Zlatomir Lukić (1982)
Publications de l'Institut Mathématique
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Hoang, C.T., Le, V.B. (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Igor' E. Zverovich, Olga I. Zverovich (2004)
Discussiones Mathematicae Graph Theory
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We introduce a new hereditary class of graphs, the dominant-matching graphs, and we characterize it in terms of forbidden induced subgraphs.
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.
Beata Orchel (1996)
Discussiones Mathematicae Graph Theory
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In this paper we give all pairs of non mutually placeable (p,q)-bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G)+e(H) ≤ 2p+q-1.
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...
Pranava K. Jha, Sandi Klavžar, Blaž Zmazek (1997)
Discussiones Mathematicae Graph Theory
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Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.
Odile Favaron, Evelyne Favaron, Zdenĕk Ryjáček (1997)
Discussiones Mathematicae Graph Theory
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The class of DCT-graphs is a common generalization of the classes of almost claw-free and quasi claw-free graphs. We prove that every even (2p+1)-connected DCT-graph G is p-extendable, i.e., every set of p independent edges of G is contained in a perfect matching of G. This result is obtained as a corollary of a stronger result concerning factor-criticality of DCT-graphs.
Grady D. Bullington, Linda L. Eroh, Steven J. Winters (2010)
Discussiones Mathematicae Graph Theory
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Explicit formulae for the γ-min and γ-max labeling values of complete bipartite graphs are given, along with γ-labelings which achieve these extremes. A recursive formula for the γ-min labeling value of any complete multipartite is also presented.