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

Naonori Kakimura, Ken Ichi Kawarabayashi, Yusuke Kobayashi

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)766-782
ページ数17
ジャーナルSIAM Journal on Discrete Mathematics
31
2
DOI
出版ステータスPublished - 2017

ASJC Scopus subject areas

  • Mathematics(all)

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