Packing A-Paths of Length Zero Modulo Four
Henning Bruhn, Arthur Ulmer
TL;DR
This paper investigates the Erdős-Pósa property for A-paths of specific lengths modulo four, establishing which lengths exhibit this property and providing new insights into their combinatorial structure.
Contribution
It proves that A-paths of length 0 and 2 modulo 4 have the Erdős-Pósa property, while those of length 1 or 3 do not, clarifying the property’s dependence on path length modulo four.
Findings
A-paths of length 0 mod 4 have the Erdős-Pósa property.
A-paths of length 2 mod 4 have the Erdős-Pósa property.
A-paths of length 1 or 3 mod 4 do not have the Erdős-Pósa property.
Abstract
We show that A-paths of length 0 modulo 4 have the Erd\H{o}s-P\'osa property. We also prove that A-paths of length 2 modulo 4 have the property but that A-paths of length 1 or of length 3 modulo 4 do not have it.
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Taxonomy
Topicsgraph theory and CDMA systems · Limits and Structures in Graph Theory · Advanced Graph Theory Research