Physical Sciences and Mathematics Commons^™

Splitter Theorems For 3- And 4-Regular Graphs, Jinko Kanno

LSU Doctoral Dissertations

Let g be a class of graphs and ≤ be a graph containment relation. A splitter theorem for g under ≤ is a result that claims the existence of a set O of graph operations such that if G and H are in g and H≤G with G≠H, then there is a decreasing sequence of graphs from G to H, say G=G₀≥G₁≥G₂...G_t=H, all intermediate graphs are in g, and each G_i can be obtained from G_i-1 by applying a single …