Computing the zig-zag number of directed graphs

Abstract The notion of zig-zag number was introduced as an attempt to provide a unified algorithmic framework for directed graphs. Nevertheless, little was known about the complexity of computing this directed graph invariant. We prove that deciding whether a directed graph has zig-zag number at most k is in NP for each fixed k ≥ 0 . Although for most of the natural decision problems this is an almost trivial result, settling k - zig-zag number in NP is surprisingly difficult. In addition, we prove that 2- zig-zag number is already an NP -hard problem.

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