Permutation-bipartition pairs

TL;DR

This paper introduces permutation-bipartition pairs, a new generalization of signed graphs and their embeddings, with applications in graph theory and surface embeddings.

Contribution

It defines permutation-bipartition pairs as a novel concept extending permutation-partition pairs, and explores their applications in graph embeddings.

Findings

Permutation-bipartition pairs generalize signed graphs.

Applications in graph embeddings are demonstrated.

Provides new tools for studying graph surface embeddings.

Abstract

Permutation-partition pairs were introduced by Stahl in 1980. These pairs are generalizations of graphs and graphs on surfaces. They were used to solve some problems for orientable embeddings of graphs. In this paper, we introduce a particular type of permutation-partition pair, called permutation-bipartition pair, which can be seen as generalizations of signed graphs and signed graph embeddings. Some applications are given.