Graphs minimal with respect to contractions in some subfamilies of maximal planar graphs
J. Florek (1987)
Applicationes Mathematicae
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J. Florek (1987)
Applicationes Mathematicae
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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...
Ilkka Holopainen, Paolo M. Soardi (1997)
Manuscripta mathematica
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Z. Majcher (1981)
Colloquium Mathematicae
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Terry A. McKee (2015)
Discussiones Mathematicae Graph Theory
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Unichord-free graphs are defined as having no cycle with a unique chord. They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to characterizing chordal graphs by minimal separators always inducing complete subgraphs). A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.
M. Giaquinta, G. Modica, J. Soucek (1993)
Manuscripta mathematica
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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)....
Petrović, Miroslav M. (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Terry A. McKee (2017)
Discussiones Mathematicae Graph Theory
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A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph).
G.L. Chia, C.S. Gan (2004)
Discussiones Mathematicae Graph Theory
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This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
H. Maehara (1991)
Discrete & computational geometry
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Jürgen Jost (1986)
Manuscripta mathematica
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P. Speissegger (1995)
Manuscripta mathematica
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Piotr Borowiecki, Jaroslav Ivančo (1997)
Discussiones Mathematicae Graph Theory
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We prove that for any two minor hereditary properties 𝓟₁ and 𝓟₂, such that 𝓟₂ covers 𝓟₁, and for any graph G ∈ 𝓟₂ there is a 𝓟₁-bipartition of G. Some remarks on minimal reducible bounds are also included.
W. Wessel (1987)
Applicationes Mathematicae
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Asit Baran-Raha (1972)
Colloquium Mathematicae
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L Moser (1959)
Acta Arithmetica
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