Graph ear decompositions and graph embeddings

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Abstract

Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximumpaired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are O (e log n)-time equivalent. This gives a polynomial time algorithm for constructing a maximum-paired ear decomposition.