Maximilian Gorsky
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126
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Combinatorics×1Discrete Math×1
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2026
An Erdős-Pósa theorem for cycles and faces of distinct lengths
This paper shows that for every graph, there exist a certain number of vertex-disjoint cycles of different lengths, or a smaller set of vertices such that the graph without these vertices has fewer cycle lengths. Similar results are proven for facial lengths of embedded graphs. The paper also shows that subdivided ladders have only a small number of cycle lengths.
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