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Removable edges in cyclically 4-edge-connected cubic graphs

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Abstract

We consider various ways of obtaining smaller cyclically 4-edge-connected cubic graphs from a given such graph. In particular, we consider removable edges: an edgee of a cyclically 4-edge-connected cubic graphG is said to be removable ifG′ is also cyclically 4-edge-connected, whereG′ is the cubic graph obtained fromG by deletinge and suppressing the two vertices of degree 2 created by the deletion. We prove that any cyclically 4-edge-connected cubic graphG with at least 12 vertices has at least 1/5(|E(G)| + 12) removable edges, and we characterize the graphs with exactly 1/5(|E(G)| + 12) removable edges.

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Authors and Affiliations

  1. Institute of Electronic Systems, Aalborg University Centre, Strandvejen 19, 4, DK 9000, Aalborg, Denmark

    Lars Døvling Andersen

  2. Austrian Academy of Science, A-1010, Vienna, Austria

    Herbert Fleischner

  3. Department of Mathematical Sciences, Goldsmiths' College, SE14 6NW, London, England

    Bill Jackson

Authors
  1. Lars Døvling Andersen
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  2. Herbert Fleischner
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  3. Bill Jackson
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Additional information

This work was carried out while the first author held a Niels Bohr Fellowship from the Royal Danish Academy of Sciences.

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Andersen, L.D., Fleischner, H. & Jackson, B. Removable edges in cyclically 4-edge-connected cubic graphs. Graphs and Combinatorics 4, 1–21 (1988). https://doi.org/10.1007/BF01864149

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  • DOI: https://doi.org/10.1007/BF01864149

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