Locally weakly confluent mappings on hereditarily locally connected continua
T. Maćkowiak (1975)
Fundamenta Mathematicae
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T. Maćkowiak (1975)
Fundamenta Mathematicae
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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...
E. Kowalska (1987)
Applicationes Mathematicae
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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...
Tanja Gologranc (2014)
Discussiones Mathematicae Graph Theory
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Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227-240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a gap in the proof of the theorem about the dismantlability of the cube graph of a tree-like partial cube and give a new proof of that result, which holds also for a bigger class of graphs, so called tree-like...
Ivan Gutman (1998)
Publications de l'Institut Mathématique
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Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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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...
Van Bang Le (2000)
Discussiones Mathematicae Graph Theory
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E. D. Tymchatyn (1976)
Colloquium Mathematicae
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B. B. Epps (1976)
Colloquium Mathematicae
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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.
Lex G. Oversteegen, Janusz R. Prajs (2003)
Fundamenta Mathematicae
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For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs,...
Kosiorek, Jaroslaw, Matras, Andrzej, Pankov, Mark (2008)
Beiträge zur Algebra und Geometrie
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