Independence Sequences of Well-Covered Graphs: Non-Unimodality and the Roller-Coaster Conjecture
نویسندگان
چکیده
A graph G is well-covered provided each maximal independent set of vertices has the same cardinality. The term sk of the independence sequence (s0, s1, . . . , sα) equals the number of independent k-sets of vertices of G. We investigate constraints on the linear orderings of the terms of the independence sequence of well-covered graphs. In particular, we provide a counterexample to the recent unimodality conjecture of Brown, Dilcher, and Nowakowski. We formulate the RollerCoaster Conjecture to describe the possible linear orderings of terms of the independence sequence.
منابع مشابه
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 2003