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• W4386974102 abstract "In the paper, we define a new parameter for tournaments called degreewidth which can be seen as a measure of how far is the tournament from being acyclic. The degreewidth of a tournament T denoted by $$varDelta (T)$$ is the minimum value k for which we can find an ordering $$langle v_1, dots , v_n rangle $$ of the vertices of T such that every vertex is incident to at most k backward arcs (i.e. an arc $$(v_i,v_j)$$ such that $$j<i$$ ). Thus, a tournament is acyclic if and only if its degreewidth is zero. Additionally, the class of sparse tournaments defined by Bessy et al. [ESA 2017] is exactly the class of tournaments with degreewidth one. We study computational complexity of finding degreewidth. We show it is NP-hard and complement this result with a 3-approximation algorithm. We provide a $$O(n^3)$$ -time algorithm to decide if a tournament is sparse, where n is its number of vertices. Finally, we study classical graph problems Dominating Set and Feedback Vertex Set parameterized by degreewidth. We show the former is fixed-parameter tractable whereas the latter is NP-hard even on sparse tournaments. Additionally, we show polynomial time algorithm for Feedback Arc Set on sparse tournaments." @default.
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• W4386974102 date "2023-01-01" @default.
• W4386974102 modified "2023-09-29" @default.
• W4386974102 title "Degreewidth: A New Parameter for Solving Problems on Tournaments" @default.
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• W4386974102 doi "https://doi.org/10.1007/978-3-031-43380-1_18" @default.
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