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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Ivica Bošnjak, Rozália Madarász (2018)
Czechoslovak Mathematical Journal
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For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.
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.