Arc-Disjoint Cycles and Feedback Arc Sets
نویسندگان
چکیده
منابع مشابه
Arc-Disjoint Cycles and Feedback Arc Sets
Isaak posed the following problem. Suppose T is a tournament having a minimum feedback arc set which induces an acyclic digraph with a hamiltonian path. Is it true that the maximum number of arc-disjoint cycles in T equals the cardinality of minimum feedback arc set of T? We prove that the answer to the problem is in the negative. Further, we study the number of arc-disjoint cycles through a ve...
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We examine the size s(n) of a smallest tournament having the arcs of an acyclic tournament on n vertices as a minimum feedback arc set. Using an integer linear programming formulation we obtain lower bounds s(n) ≥ 3n − 2 − blog2 nc or s(n) ≥ 3n − 1 − blog2 nc, depending on the binary expansion of n. When n = 2k − 2t we show that the bounds are tight with s(n) = 3n−2−blog2 nc. One view of this p...
متن کاملThe Parameterized Complexity of Packing Arc-Disjoint Cycles in Tournaments
Given a directed graph D on n vertices and a positive integer k, the Arc-Disjoint Cycle Packing problem is to determine whether D has k arc-disjoint cycles. This problem is known to be W[1]-hard in general directed graphs. In this paper, we initiate a systematic study on the parameterized complexity of the problem restricted to tournaments. We show that the problem is fixed-parameter tractable ...
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A feedback vertex set/arc set (abbreviated to FVS/FAS) is a vertex/arc subset of a graph whose removal induces the remaining graph acyclic. A minimum FVS/FAS is an FVS/FAS which contains the smallest number of vertices/arcs. Hsu and Lin [8] first proposed an algorithm which can find a minimum FVS in rotator graphs. In this paper, we present two efficient algorithms both of which construct FAS’s...
متن کاملLarge Feedback Arc Sets, High Minimum Degree Subgraphs, and Long Cycles in Eulerian Digraphs
HAO HUANG1† , J IE MA, ASAF SHAPIRA3‡, BENNY SUDAKOV4§ and RAPHAEL YUSTER 1Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail: [email protected]) 2Department of Mathematics, UCLA, Los Angeles, CA 90095, USA (e-mail: [email protected]) 3School of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: [email protected]) 4Department of Mathematics, ETH, 8092 Zuri...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2013
ISSN: 0364-9024
DOI: 10.1002/jgt.21742