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Splitter Theorems for 4-Regular Graphs

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Abstract

Let \({\Phi_{k,g}}\) be the class of all k-edge connected 4-regular graphs with girth of at least g. For several choices of k and g, we determine a set \({\mathcal{O}_{k,g}}\) of graph operations, for which, if G and H are graphs in \({\Phi_{k,g}}\), G ≠ H, and G contains H as an immersion, then some operation in \({\mathcal{O}_{k,g}}\) can be applied to G to result in a smaller graph G′ in \({\Phi_{k,g}}\) such that, on one hand, G′ is immersed in G, and on the other hand, G′ contains H as an immersion.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Guoli Ding

  2. Mathematics and Statistics Program, Louisiana Tech University, Ruston, LA, 71272, USA

    Jinko Kanno

Authors
  1. Guoli Ding
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  2. Jinko Kanno
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Correspondence to Guoli Ding.

Additional information

G. Ding’s research was partially supported by NSF grant DMS-0556091 and J. Kanno’s research was partially supported by Board of Regents grant LEQSF(2004-07)-RD-A-22.

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Ding, G., Kanno, J. Splitter Theorems for 4-Regular Graphs. Graphs and Combinatorics 26, 329–344 (2010). https://doi.org/10.1007/s00373-010-0916-y

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