On weights of induced paths and cycles in claw-free and K1, r-free graphs
نویسندگان
چکیده
Let G be a K 1;r-free graph (r 3) on n vertices. We prove that, for any induced path or induced cycle on k vertices in G (k 2r ? 1 or k 2r, respectively), the degree sum of its vertices is at most (2r ? 2)(n ?) where is the independence number of G. As a corollary we obtain an upper bound on the length of a longest induced path and a longest induced cycle in a K 1;r-free graph. Stronger bounds are given in the special case of claw-free graphs (i.e. r = 3). Sharpness examples are also presented. c
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عنوان ژورنال:
- Journal of Graph Theory
دوره 36 شماره
صفحات -
تاریخ انتشار 2001