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Girth Six Cubic Graphs Have Petersen Minors

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Abstract

We prove that every 3-regular graph with no circuit of length less than six has a subgraph isomorphic to a subdivision of the Petersen graph.

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Authors and Affiliations

  1. Department of Mathematics, Ohio State University, 231 W. 18th Ave., Columbus, Ohio, 43210, USA

    Neil Robertson

  2. Department of Mathematics, Princeton University, Princeton, New Jersey, 08544, USA

    P. D. Seymour

  3. School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, 30332, USA

    Robin Thomas

Authors
  1. Neil Robertson
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  2. P. D. Seymour
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  3. Robin Thomas
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Corresponding authors

Correspondence to Neil Robertson, P. D. Seymour or Robin Thomas.

Additional information

Research partially performed under a consulting agreement with Bellcore, 445 South St., Morristown, New Jersey 07960, USA, and partially supported by DIMACS Center, Rutgers University, New Brunswick, New Jersey 08903, USA.

Partially supported by NSF under Grant No. DMS-9401981 and by ONR under Grant No. N00014-92-J-1965.

Research partially performed while Seymour was employed at Bellcore, and partially supported by ONR grant N00014-10-1-0680, and NSF grants DMS-1265563 and DMS-1800053.

Partially supported by NSF under Grants No. DMS-9623031, DMS-1202640 and DMS- 1700157 and by ONR under Contract No. N00014-93-1-0325.

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Robertson, N., Seymour, P.D. & Thomas, R. Girth Six Cubic Graphs Have Petersen Minors. Combinatorica 39, 1413–1423 (2019). https://doi.org/10.1007/s00493-019-3268-0

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  • DOI: https://doi.org/10.1007/s00493-019-3268-0

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