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Uniquely C 4-Saturated Graphs

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Abstract

For a fixed graph H, a graph G is uniquely H-saturated if G does not contain H, but the addition of any edge from \({\overline{G}}\) to G completes exactly one copy of H. Using a combination of algebraic methods and counting arguments, we determine all the uniquely C 4-saturated graphs; there are only ten of them.

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Authors and Affiliations

  1. Mathematics Department, University of South Carolina, Columbia, SC, USA

    Joshua Cooper

  2. Mathematics Department, University of Illinois, Urbana, IL, USA

    John Lenz, Timothy D. LeSaulnier & Douglas B. West

  3. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO, USA

    Paul S. Wenger

Authors
  1. Joshua Cooper
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  2. John Lenz
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  3. Timothy D. LeSaulnier
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  4. Paul S. Wenger
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  5. Douglas B. West
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Corresponding author

Correspondence to Paul S. Wenger.

Additional information

Research of all authors partially supported by NSF grant DMS 08-38434 “EMSW21-MCTP: Research Experience for Graduate Students.”

Douglas B. West’s Research supported by NSA grant H98230-09-1-0363.

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Cooper, J., Lenz, J., LeSaulnier, T.D. et al. Uniquely C 4-Saturated Graphs. Graphs and Combinatorics 28, 189–197 (2012). https://doi.org/10.1007/s00373-011-1038-x

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  • DOI: https://doi.org/10.1007/s00373-011-1038-x

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