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Split graphs of Dilworth number 2. (English) Zbl 0573.05047

In this paper is given a short outline of results concerning to graphs with Dilworth number at most 2. There is proved the equivalence of split graphs with Dilworth number at most 2 and the class of graphs G such that G and its complement \(\bar G\) are interval graphs. There is also given a characterisation of such graphs by means of forbidden graphs.
Reviewer: L.Niepel

MSC:

05C99 Graph theory
Full Text: DOI

References:

[1] Akiyama, J.; Ando, K.; Harary, F., A graph and its complement with specified properties VIII: interval graphs, Mimeograph (1983)
[2] C. Benzaken, P.L. Hammer and D. de Werra, Threshold characterization of graphs with Dilworth number two, J. Graph Theory, to appear.; C. Benzaken, P.L. Hammer and D. de Werra, Threshold characterization of graphs with Dilworth number two, J. Graph Theory, to appear. · Zbl 0583.05048
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[5] Foldes, S.; Hammer, P. L., Split graphs having Dilworth number 2, Canad. J. Math., 29, 666-672 (1977) · Zbl 0335.05130
[6] Gilmore, P. C.; Hoffman, A., A characterization of comparability graphs and of interval graphs, Canad. J. Math., 16, 539-548 (1964) · Zbl 0121.26003
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