Splitter Theorems for 4-Regular Graphs |
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Authors: | Guoli Ding Jinko Kanno |
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Institution: | 1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA 2. Mathematics and Statistics Program, Louisiana Tech University, Ruston, LA, 71272, USA
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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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