Erdős-Pósa property of chordless cycles and its applications
Kim, Eun Jung; Kwon, O-joung (2018), Erdős-Pósa property of chordless cycles and its applications, in Czumaj, Artur, Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 18), Society for Industrial and Applied Mathematics, p. 1665-1684. 10.1137/1.9781611975031.109
TypeCommunication / Conférence
External document linkhttps://arxiv.org/abs/1711.00667v2
Conference title29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 18)
Conference cityNew Orleans, Louisiana
Conference countryUnited States
Book titleProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 18)
Book authorCzumaj, Artur
Number of pages2764
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Author(s)Kim, Eun Jung
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)A chordless cycle in a graph G is an induced subgraph of G which is a cycle of length at least four. We prove that the Erdős-Pósa property holds for chordless cycles, which resolves the major open question concerning the Erdős-Pósa property. Our proof for chordless cycles is constructive: in polynomial time, one can find either k + 1 vertex-disjoint chordless cycles, or ck2 log k vertices hitting every chordless cycle for some constant c. It immediately implies an approximation algorithm of factor O(opt log opt) for Chordal Vertex Deletion. We complement our main result by showing that chordless cycles of length at least ℓ for any fixed ℓ ≥ 5 do not have the Erdős-Pósa property.As a corollary, for a non-negative integral function w defined on the vertex set of a graph G, the minimum value Σx∊S w(x) over all vertex sets S hitting all cycles of G is at most O(k2 log k) where k is the maximum number of cycles (not necessarily vertex-disjoint) in G such that each vertex υ is used at most w(υ) times.
Subjects / KeywordsGraphs
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