A note on randomly complete -partite graphs
Pavol Híc (1992)
Mathematica Slovaca
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Pavol Híc (1992)
Mathematica Slovaca
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Ferdinand Gliviak (1997)
Mathematica Bohemica
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A graph is called an -graph if its periphery is equal to its center eccentric vertices . Further, a graph is called a -graph if . We describe -graphs and -graphs for small radius. Then, for a given graph and natural numbers , , we construct an -graph of radius having central vertices and containing as an induced subgraph. We prove an analogous existence theorem for -graphs, too. At the end, we give some properties of -graphs and -graphs.
Jozef Bucko, Peter Mihók (2009)
Discussiones Mathematicae Graph Theory
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A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property is of finite character if a graph G has a property if and only if every finite induced subgraph of G has a property . Let ₁,₂,...,ₙ be graph properties of finite character, a graph G is said to be (uniquely) (₁, ₂, ...,ₙ)-partitionable if there is an (exactly one) partition V₁, V₂, ..., Vₙ of V(G) such that for i = 1,2,...,n. Let us denote by ℜ = ₁ ∘ ₂ ∘ ... ∘ ₙ the class...
Bert Randerath, Preben Dahl Vestergaard (2002)
Discussiones Mathematicae Graph Theory
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A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer [14] defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. One of the most challenging problems in this area, posed in the survey of Plummer [15], is to find a good characterization of well-covered graphs of girth 4. We examine several subclasses of well-covered graphs of girth ≥ 4 with respect to the odd girth...
Allan Bickle (2013)
Mathematica Bohemica
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The -core of a graph , , is the maximal induced subgraph such that , if it exists. For , the -shell of a graph is the subgraph of induced by the edges contained in the -core and not contained in the -core. The core number of a vertex is the largest value for such that , and the maximum core number of a graph, , is the maximum of the core numbers of the vertices of . A graph is -monocore if . This paper discusses some basic results on the structure of -cores and...
Peter Kyš (2000)
Mathematica Bohemica
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The eccentricity of a vertex is the distance from to a vertex farthest from , and is an eccentric vertex for if its distance from is . A vertex of maximum eccentricity in a graph is called peripheral, and the set of all such vertices is the peripherian, denoted . We use to denote the set of eccentric vertices of vertices in . A graph is called an S-graph if . In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of...