TY - JOUR

T1 - Packing edge-disjoint odd Eulerian subgraphs through prescribed vertices in 4-edge-connected graphs

AU - Kakimura, Naonori

AU - Kawarabayashi, Ken Ichi

AU - Kobayashi, Yusuke

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, we show the Erdos-Pósa property for edge-disjoint packing of S-closed walks with parity constraints in 4-edge-connected graphs. More precisely, we prove that for any 4-edge-connected graph G and any vertex subset S, either G has k edge-disjoint elementary closed odd walks, each of which has at least one vertex of S, or G has an edge set F with |F| ≥ f(k) such that G - F has no such walks. The 4-edge-connectivity is the best possible in the sense that 3-edge-connected graphs do not satisfy the statement. Since the proof is constructive, we can design a fixed-parameter algorithm for finding k edge-disjoint walks satisfying the conditions in a 4-edge-connected graph for a parameter k. In addition, this gives a simple fixed-parameter algorithm for the parity edge-disjoint walks problem with k terminal pairs.

AB - In this paper, we show the Erdos-Pósa property for edge-disjoint packing of S-closed walks with parity constraints in 4-edge-connected graphs. More precisely, we prove that for any 4-edge-connected graph G and any vertex subset S, either G has k edge-disjoint elementary closed odd walks, each of which has at least one vertex of S, or G has an edge set F with |F| ≥ f(k) such that G - F has no such walks. The 4-edge-connectivity is the best possible in the sense that 3-edge-connected graphs do not satisfy the statement. Since the proof is constructive, we can design a fixed-parameter algorithm for finding k edge-disjoint walks satisfying the conditions in a 4-edge-connected graph for a parameter k. In addition, this gives a simple fixed-parameter algorithm for the parity edge-disjoint walks problem with k terminal pairs.

KW - Cycle packing

KW - Erdos-Pósa property

KW - Fixed-parameter algorithm

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U2 - 10.1137/15M1022239

DO - 10.1137/15M1022239

M3 - Article

AN - SCOPUS:85021888664

VL - 31

SP - 766

EP - 782

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -