Splitter Theorems for 4-Regular Graphs

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• 作者：Guoli Ding and Jinko Kanno
• 关键词：Splitter theorem ; Immersion ; 4 ; Regular graphs ; Generating theorem ; Graph operations
• 刊名：Graphs and Combinatorics
• 出版时间：May, 2010
• 出版年：2010
• 期刊代码：63_0911-0119
• 类别：mat
• 卷：26
• 期：3
• 页码：329-344
• 数据来源：sp

摘要

Let F_k,g{\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 O_k,g{\mathcal{O}_{k,g}} of graph operations, for which, if G and H are graphs in F_k,g{\Phi_{k,g}}, G ≠ H, and G contains H as an immersion, then some operation in O_k,g{\mathcal{O}_{k,g}} can be applied to G to result in a smaller graph G′ in F_k,g{\Phi_{k,g}} such that, on one hand, G′ is immersed in G, and on the other hand, G′ contains H as an immersion.