Displaying similar documents to “Some additions to the theory of star partitions of graphs”

γ-labelings of complete bipartite graphs

Grady D. Bullington, Linda L. Eroh, Steven J. Winters (2010)

Discussiones Mathematicae Graph Theory

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Explicit formulae for the γ-min and γ-max labeling values of complete bipartite graphs are given, along with γ-labelings which achieve these extremes. A recursive formula for the γ-min labeling value of any complete multipartite is also presented.

On partitions of hereditary properties of graphs

Mieczysław Borowiecki, Anna Fiedorowicz (2006)

Discussiones Mathematicae Graph Theory

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In this paper a concept 𝓠-Ramsey Class of graphs is introduced, where 𝓠 is a class of bipartite graphs. It is a generalization of well-known concept of Ramsey Class of graphs. Some 𝓠-Ramsey Classes of graphs are presented (Theorem 1 and 2). We proved that 𝓣₂, the class of all outerplanar graphs, is not 𝓓₁-Ramsey Class (Theorem 3). This results leads us to the concept of acyclic reducible bounds for a hereditary property 𝓟 . For 𝓣₂ we found two bounds (Theorem 4). An improvement,...

Remarks on the existence of uniquely partitionable planar graphs

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".

Dominant-matching graphs

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.