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.

Some globally determined classes of graphs

Ivica Bošnjak, Rozália Madarász (2018)

Czechoslovak Mathematical Journal

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For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.

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.