Displaying similar documents to “Maximal graphs with respect to hereditary properties”

On hereditary properties of composition graphs

Vadim E. Levit, Eugen Mandrescu (1998)

Discussiones Mathematicae Graph Theory

Similarity:

The composition graph of a family of n+1 disjoint graphs H i : 0 ≤ i ≤ n is the graph H obtained by substituting the n vertices of H₀ respectively by the graphs H₁,H₂,...,Hₙ. If H has some hereditary property P, then necessarily all its factors enjoy the same property. For some sort of graphs it is sufficient that all factors H i : 0 ≤ i ≤ n have a certain common P to endow H with this P. For instance, it is known that the composition graph of a family of perfect graphs is also a perfect graph (B. Bollobas, 1978),...

On generating sets of induced-hereditary properties

Gabriel Semanišin (2002)

Discussiones Mathematicae Graph Theory

Similarity:

A natural generalization of the fundamental graph vertex-colouring problem leads to the class of problems known as generalized or improper colourings. These problems can be very well described in the language of reducible (induced) hereditary properties of graphs. It turned out that a very useful tool for the unique determination of these properties are generating sets. In this paper we focus on the structure of specific generating sets which provide the base for the proof of The Unique...

On graphs with maximum size in their switching classes

Sergiy Kozerenko (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In his PhD thesis [Structural aspects of switching classes, Leiden Institute of Advanced Computer Science, 2001] Hage posed the following problem: “characterize the maximum size graphs in switching classes”. These are called s-maximal graphs. In this paper, we study the properties of such graphs. In particular, we show that any graph with sufficiently large minimum degree is s-maximal, we prove that join of two s-maximal graphs is also an s-maximal graph, we give complete characterization...

Arithmetically maximal independent sets in infinite graphs

Stanisław Bylka (2005)

Discussiones Mathematicae Graph Theory

Similarity:

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.

Radio Graceful Hamming Graphs

Amanda Niedzialomski (2016)

Discussiones Mathematicae Graph Theory

Similarity:

For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...

Generalized domination, independence and irredudance in graphs

Mieczysław Borowiecki, Danuta Michalak, Elżbieta Sidorowicz (1997)

Discussiones Mathematicae Graph Theory

Similarity:

The purpose of this paper is to present some basic properties of 𝓟-dominating, 𝓟-independent, and 𝓟-irredundant sets in graphs which generalize well-known properties of dominating, independent and irredundant sets, respectively.

Graphs maximal with respect to hom-properties

Jan Kratochvíl, Peter Mihók, Gabriel Semanišin (1997)

Discussiones Mathematicae Graph Theory

Similarity:

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.

A note on maximal common subgraphs of the Dirac's family of graphs

Jozef Bucko, Peter Mihók, Jean-François Saclé, Mariusz Woźniak (2005)

Discussiones Mathematicae Graph Theory

Similarity:

Let ⁿ be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set ⁿ is a common subgraph F of order n of each member of ⁿ, that is not properly contained in any larger common subgraph of each member of ⁿ. By well-known Dirac’s Theorem, the Dirac’s family ⁿ of the graphs of order n and minimum degree δ ≥ [n/2] has a maximal common subgraph containing Cₙ. In this note we study the problem of determining all maximal common subgraphs of the Dirac’s...

Bounding the Openk-Monopoly Number of Strong Product Graphs

Dorota Kuziak, Iztok Peterin, Ismael G. Yero (2018)

Discussiones Mathematicae Graph Theory

Similarity:

Let G = (V, E) be a simple graph without isolated vertices and minimum degree δ, and let k ∈ 1 − ⌈δ/2⌉, . . . , ⌊δ/2⌋ be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if [...] δM(v)≥δG(v)2+k δ M ( v ) ≥ δ G ( v ) 2 + k , where δM(v) represents the number of neighbors of v in M and δG(v) the degree of v in G. A set M is called an open k-monopoly if every vertex v of G is k-controlled by M. The minimum cardinality of any open k-monopoly is the open k-monopoly number of G. In this...

Unique factorization theorem

Peter Mihók (2000)

Discussiones Mathematicae Graph Theory

Similarity:

A property of graphs is any class of graphs closed under isomorphism. A property of graphs is induced-hereditary and additive if it is closed under taking induced subgraphs and disjoint unions of graphs, respectively. Let ₁,₂, ...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable (G has property ₁ º₂ º... ºₙ) if the vertex set V(G) of G can be partitioned into n sets V₁,V₂,..., Vₙ such that the subgraph G [ V i ] of G induced by Vi belongs to i ; i = 1,2,...,n. A property is said...

k -Ramsey classes and dimensions of graphs

Jan Kratochvíl (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this note, we introduce the notion of k -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.