منابع مشابه
Packing Odd Circuits
We determine the structure of a class of graphs that do not contain the complete graph on five vertices as a “signed minor.” The result says that each graph in this class can be decomposed into elementary building blocks in which maximum packings by odd circuits can be found by flow or matching techniques. This allows us to actually find a largest collection of pairwise edge disjoint odd circui...
متن کاملPacking Odd Circuits in Eulerian Graphs
Let C be the clutter of odd circuits of a signed graph ðG;SÞ: For nonnegative integral edge-weights w; we are interested in the linear program minðwtx: xðCÞ51; for C 2 C; and x50Þ; which we denote by (P). The problem of solving the related integer program clearly contains the maximum cut problem, which is NP-hard. Guenin proved that (P) has an optimal solution that is integral so long as ðG;SÞ ...
متن کاملPacking circuits in matroids
The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: For any nonnegative integral weight function w defined on E(M), Maximum {k : M has k circuits (repetition allowed) such that each element e of M is used at most 2w(e) times by these circuits} = Minimum {x∈X w(x) : X is a collection of elements (repetition allowed) of M such that every circui...
متن کاملPacking Circuits into K
We shall pack circuits of arbitrary lengths into the complete graph KN . More precisely, if N is odd and ∑t i=1 mi = (N 2 ) , mi ≥ 3, then the edges of KN can be written as an edge disjoint union of circuits of lengths m1, . . . , mt. Since the degrees of the vertices in any such packing must be even, this result cannot hold for even N . For N even, we prove that if ∑t i=1 mi ≤ (N 2 )− N 2 then...
متن کاملPacking Directed Circuits
We prove a conjecture of Younger, that for every integer n ≥ 0 there exists an integer t ≥ 0 such that for every digraph G, either G has n vertex-disjoint directed circuits, or G can be made acyclic by deleting at most t vertices.
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2007
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480198345405