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BOUNDS FOR THE INDEPENDENCE NUMBER OF CRITICAL GRAPHS

Published online by Cambridge University Press:  01 March 2000

GUNNAR BRINKMANN ,
SHESHAYYA A. CHOUDUM ,
STEFAN GRÜNEWALD  and
ECKHARD STEFFEN
GUNNAR BRINKMANN
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
SHESHAYYA A. CHOUDUM
Affiliation:
Department of Mathematics, Indian Institute of Technology, Madras 600 036, India
STEFAN GRÜNEWALD
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
ECKHARD STEFFEN
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
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Abstract

In 1968 Vizing conjectured that any independent vertex set of an edge-chromatic critical graph G contains at most half of the vertices of G, that is, α(G) [les ] ½[mid ]V(G)[mid ]. Let Δ be the maximum vertex degree in a critical graph. For each Δ, we determine c(Δ) such that α(G) [les ] c(Δ)[mid ]V)[mid ].

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 2 , March 2000 , pp. 137 - 140
Copyright
© The London Mathematical Society 2000

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