Asymptotics of the extremal values of certain graph parameters in trees with bounded degree

• Autores: Clemens Heuberger, Stephan G. Wagner
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 77, Fasc. 3-4, 2010, págs. 347-368
• Idioma: inglés
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• Resumen

  • Year: 2010 Vol.: 77 Fasc.: 3-4 Title: Asymptotics of the extremal values of certain graph parameters in trees with bounded degree Author(s): Clemens Heuberger and Stephan G. Wagner In a recent paper, the authors of this note determined the trees of given maximum degree which maximize the number of independent vertex subsets and minimize the number of independent edge subsets respectively. It turned out that some kind of digit representation plays a major role in the characterization of the optimal trees.

    In the current paper, we study the asymptotic behavior of the optimal parameter values. It turns out that they increase exponentially, but with °uctuations which can be described by means of the aforementioned digit system.

    Address:

    Clemens Heuberger Institut fÄur Mathematik B Technische UniversitÄat Graz Austria Address:

    Stephan G. Wagner Department of Mathematical Sciences Stellenbosch University South Africa