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Split Graphs with Specified Dilworth Numbers

Published online by Cambridge University Press:  20 November 2018

Chiê Nara  and
Iwao Sato
Chiê Nara
Affiliation:
Department of Mathematics, Musashi Institute of Technology, Tamazutsumi, Setagaya-Ku, Tokyo 158,Japan
Iwao Sato
Affiliation:
Tsuruoka Technical College, 104 Sawata, Aza, Ioka, Óaza, Tsuruoka City 997, Japan
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Abstract

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Let G be a split graph with the independent part IG and the complete part KG. Suppose that the Dilworth number of (IG, ≼) with respect to the vicinal preorder ≼ is two and that of (KG, ≼) is an integer k. We show that G has a specified graph Hk, defined in this paper, as an induced subgraph.

Keywords

05C75
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 43 - 47
Copyright
Copyright © Canadian Mathematical Society 1984

References

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