A note on intersecting graphs.
Bretto, A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Bretto, A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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W. Wessel (1987)
Applicationes Mathematicae
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Mieczysław Borowiecki, Peter Mihók, Zsolt Tuza, M. Voigt (1999)
Discussiones Mathematicae Graph Theory
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We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (𝓓₁,𝓓₁)-partitionable planar graphs with respect to the property 𝓓₁ "to be a forest".
Zdzisław Skupień (2007)
Discussiones Mathematicae Graph Theory
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Terry A. McKee (2018)
Discussiones Mathematicae Graph Theory
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Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the classical chordal graphs and the emergent unichord-free graphs. New theorems characterize several subclasses of the graphs whose minimal separators induce complete multipartite subgraphs, in particular the graphs that are 2-clique sums...
Risto Šokarovski (1977)
Publications de l'Institut Mathématique
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Gary Chartrand, Hudson V. Kronk, Seymour Schuster (1973)
Colloquium Mathematicae
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Jan Kratochvíl, Peter Mihók, Gabriel Semanišin (1997)
Discussiones Mathematicae Graph Theory
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For a simple graph H, →H denotes the class of all graphs that admit homomorphisms to H (such classes of graphs are called hom-properties). We investigate hom-properties from the point of view of the lattice of hereditary properties. In particular, we are interested in characterization of maximal graphs belonging to →H. We also provide a description of graphs maximal with respect to reducible hom-properties and determine the maximum number of edges of graphs belonging to →H.
Lynch, Christopher, Strogova Polina (1998)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Mohammad Hadi Shekarriz, Madjid Mirzavaziri, Kamyar Mirzavaziri (2018)
Discussiones Mathematicae Graph Theory
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A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing specialized bi-independent covering (SBIC) and a structure named generalized complete bipartite graph (GCBG)....
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.
Stanisław Bylka (2005)
Discussiones Mathematicae Graph Theory
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Families of all sets of independent vertices in graphs are investigated. The problem how to characterize those infinite graphs which have arithmetically maximal independent sets is posed. A positive answer is given to the following classes of infinite graphs: bipartite graphs, line graphs and graphs having locally infinite clique-cover of vertices. Some counter examples are presented.