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

Naonori Kakimura, Ken Ichi Kawarabayashi, Yusuke Kobayashi

Research output: Contribution to journalArticle

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)766-782
Number of pages17
JournalSIAM Journal on Discrete Mathematics
Issue number2
Publication statusPublished - 2017 Jan 1



  • Cycle packing
  • Erdos-Pósa property
  • Fixed-parameter algorithm

ASJC Scopus subject areas

  • Mathematics(all)

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