Fundamental Cycles and Graph Embeddings

TL;DR

This paper introduces a new characterization of the maximum genus of a graph, generalizing previous work, and provides a polynomial-time algorithm for computing it.

Contribution

It presents a novel good characterization of maximum genus that unifies earlier results and offers an efficient algorithm for its determination.

Findings

New characterization of maximum genus

Polynomial-time algorithm for maximum genus

Generalization of previous theories

Abstract

In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al. Based on this, we find a new polynomially bounded algorithm to find the maximum genus of a graph.