Packing $A$-paths of length zero modulo a prime

DOI10.1016/J.JCTB.2022.12.007arXiv2009.12230MaRDI QIDQ6349883

Robin Thomas, Youngho Yoo

Publication date: 23 September 2020

Abstract: It is known that $A$-paths of length $0$ mod $m$ satisfy the ErdH{o}s-P'osa property if $m=2$ or $m=4$, but not if $m>4$ is composite. We show that if $p$ is prime, then $A$-paths of length $0$ mod $p$ satisfy the ErdH{o}s-P'osa property. More generally, in the framework of undirected group-labelled graphs, we characterize the abelian groups $Gamma$ and elements $ellinGamma$ for which the ErdH{o}s-P'osa property holds for $A$-paths of weight $ell$.

Mathematics Subject Classification ID

Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

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