Discussiones Mathematicae Graph Theory 29(2) (2009) 377-383
doi: 10.7151/dmgt.1453

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ON F-INDEPENDENCE IN GRAPHS

Frank Göring

Fakultät für Mathematik
TU Chemnitz, 09107 Chemnitz, Germany
e-mail: frank.goering@mathematik.tu-chemnitz.de

Jochen Harant, Dieter Rautenbach

Institut für Mathematik
TU Ilmenau, Postfach 100565, 98684 Ilmenau, Germany
e-mail: jochen.harant@tu-ilmenau.de
e-mail: dieter.rautenbach@tu-ilmenau.de

Ingo Schiermeyer

Institut für Diskrete Mathematik und Algebra
TU Bergakademie Freiberg, 09596 Freiberg, Germany
e-mail: schierme@math.tu-freiberg.de

Abstract

Let F be a set of graphs and for a graph G let αF(G) and α F*(G) denote the maximum order of an induced subgraph of G which does not contain a graph in F as a subgraph and which does not contain a graph in F as an induced subgraph, respectively. Lower bounds on αF(G) and αF*(G) are presented.

Keywords: independence, complexity, probabilistic method.

2000 Mathematics Subject Classification: 05C69.

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Received 25 March 2008
Revised 26 March 2008
Accepted 23 May 2008