Ramsey-Type Results for Unions of Comparability Graphs
نویسندگان
چکیده
It is well known that the comparability graph of any partially ordered set of n elements contains either a clique or an independent set of size at least pn. In this note we show that any graph of n vertices which is the union of two comparability graphs on the same vertex set, contains either a clique or an independent set of size at least n 13 . On the other hand, there exist such graphs for which the size of any clique or independent set is at most n0:4118. Similar results are obtained for graphs which are unions of a xed number k comparability graphs. We also show that the same bounds hold for unions of perfect graphs.
منابع مشابه
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 18 شماره
صفحات -
تاریخ انتشار 2002