Analysis of Embedding and Extensions in Topological Graph Theory

Abstract

Topological Graph Theory (TGT) is a branch of mathematics that studies the interplay between graphs and topology. We discuss how embeddings and extensions affect multiple exports and minimal in minor-closed two-sum families of graphs—charts with limited treewidth that use recursive edge replacement fall under this category. We improve upon the TGT prior upper limit of fourteen established and, showing that any graph eliminating  K4 as a minor and described by Seymour, in particular parallel-series graphs, may be embedded into L1 was recently discovered with a distortion of at most two, the upper bound of two is optimum.