Proof of Berge's path partition conjecture for k ≤ λ - 3
نویسنده
چکیده
Let D be a digraph. A path partition of D is called k-optimal if the sum of the k-norms of its paths isminimal. The k-norm of a path P ismin(|V (P)|, k). Berge’s path partition conjecture claims that for every k-optimal path partition P there are k disjoint stable sets orthogonal to P . For general digraphs the conjecture has been proven for k = 1, 2, λ − 1, λ, where λ is the length of a longest path in the digraph. In this paper we prove the conjecture for λ − 2 and λ − 3. © 2015 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 209 شماره
صفحات -
تاریخ انتشار 2016