The Extremal Function for Bipartite Linklessly Embeddable Graphs

Abstract

An embedding of a graph in 3-space is linkless if for every two disjoint cycles there exists an embedded ball that contains one of the cycles and is disjoint from the other. We prove that every bipartite linklessly embeddable (simple) graph on n ≥ 5 vertices has at most 3n - 10 edges, unless it is isomorphic to the complete bipartite graph K3,n-3.

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Acknowledgment

We would like to thank two anonymous referees for carefully reading the manuscript and for providing many helpful suggestions.

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Correspondence to Rose McCarty.

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Partially supported by NSF under Grants No. DMS-1202640 and DMS-1700157.

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McCarty, R., Thomas, R. The Extremal Function for Bipartite Linklessly Embeddable Graphs. Combinatorica 39, 1081–1104 (2019). https://doi.org/10.1007/s00493-019-3856-z

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Mathematics Subject Classification (2010)

  • 05C35
  • 05C10
  • 05C83