Independence complexes of claw-free graphs
نویسنده
چکیده
We study the class of independence complexes of claw-free graphs. The main theorem give good bounds on the connectivity of these complexes, given bounds for a few subcomplexes of the same class. Two applications are presented. Firstly, we show that the independence complex of a claw-free graph with n vertices and maximal degree d is (cn/d + ε)–connected, where c = 2/3. This can be compared with the result of Szabó and Tardos that c = 1/2 is optimal with no restrictions on the graphs. Secondly, we calculate the connectivity of a family of complexes used in Babson and Kozlov’s proof of Lovász conjecture.
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 29 شماره
صفحات -
تاریخ انتشار 2008