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- W3088215122 abstract "We prove a refinement of the flat wall theorem of Robertson and Seymour to undirected group-labelled graphs (G,γ) where γ assigns to each edge of an undirected graph G an element of an abelian group Γ. As a consequence, we prove that Γ-nonzero cycles (cycles whose edge labels sum to a non-identity element of Γ) satisfy the half-integral Erdős-Pósa property, and we also recover a result of Wollan that if Γ has no element of order two, then Γ-nonzero cycles satisfy the Erdős-Pósa property. As another application, we prove that if m is an odd prime power, then cycles of length ℓmodm satisfy the Erdős-Pósa property for all integers ℓ. This partially answers a question of Dejter and Neumann-Lara from 1987 on characterizing all such integer pairs (ℓ,m)." @default.
- W3088215122 created "2020-10-01" @default.
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- W3088215122 date "2023-07-01" @default.
- W3088215122 modified "2023-09-25" @default.
- W3088215122 title "Packing cycles in undirected group-labelled graphs" @default.
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- W3088215122 doi "https://doi.org/10.1016/j.jctb.2023.02.011" @default.
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