Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-11T04:55:11.262Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Chvátal, V. and Hammer, P. L., Set-packing problem and threshold graph, Univ. of Waterloo, CORR 73-21, August 1973.Google Scholar
2. Dilworth, R. P., A decomposition theorem for partially ordered sets, Ann. of Math. 51 (1950), 161-166.Google Scholar
3. Foldes, S. and Hammer, P. L., Split graphs having Dilworth number two, Can. J. of Math. Vol. 29 (1977), 666-672.Google Scholar
4. Nara, C., Split graphs with Dilworth number three, Nat. Sci. Rep. Ochanomizu Univ., Vol. 33 (1982), 37-44.Google Scholar