A Tighter Erdős‐Pósa Function for Long Cycles | Zendy

Fiorini Samuel | Zendy; Herinckx Audrey | Zendy

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A Tighter Erdős‐Pósa Function for Long Cycles

Author(s) -

Fiorini Samuel,

Herinckx Audrey

Publication year - 2014

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.21776

Subject(s) - combinatorics , mathematics , disjoint sets , bivariate analysis , vertex (graph theory) , graph , function (biology) , discrete mathematics , statistics , evolutionary biology , biology

We prove that there exists a bivariate function f with f ( k , ℓ ) = O ( ℓ · k log k ) such that for every natural k and ℓ, every graph G has at least k vertex‐disjoint cycles of length at least ℓ or a set of at most f ( k , ℓ ) vertices that meets all cycles of length at least ℓ. This improves a result by Birmelé et al. (Combinatorica, 27 (2007), 135–145), who proved the same result with f ( k , ℓ ) = Θ ( ℓ · k 2 ) .

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