Displaying similar documents to “Structural results on maximal k-degenerate graphs”

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.

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...

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.

Gamma Graphs Of Some Special Classes Of Trees

Anna Bień (2015)

Annales Mathematicae Silesianae

Similarity:

A set S ⊂ V is a dominating set of a graph G = (V, E) if every vertex υ ∈ V which does not belong to S has a neighbour in S. The domination number γ(G) of the graph G is the minimum cardinality of a dominating set in G. A dominating set S is a γ-set in G if |S| = γ(G). Some graphs have exponentially many γ-sets, hence it is worth to ask a question if a γ-set can be obtained by some transformations from another γ-set. The study of gamma graphs is an answer to this reconfiguration problem....

The Thickness of Amalgamations and Cartesian Product of Graphs

Yan Yang, Yichao Chen (2017)

Discussiones Mathematicae Graph Theory

Similarity:

The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study...

A characterization of complete tripartite degree-magic graphs

Ľudmila Bezegová, Jaroslav Ivančo (2012)

Discussiones Mathematicae Graph Theory

Similarity:

A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.

Supermagic Generalized Double Graphs 1

Jaroslav Ivančo (2016)

Discussiones Mathematicae Graph Theory

Similarity:

A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.

Graphs of low chordality.

Chandran, L.Sunil, Lozin, Vadim V., Subramanian, C.R. (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Similarity: