Deficiency in Signed Graphs

TL;DR

This paper introduces the concept of deficiency in signed graphs, classifies deficiency for 2-chromatic graphs, and provides polynomial algorithms for certain deficiency decision problems in 3-chromatic signed graphs.

Contribution

It defines deficiency in signed graphs, classifies it for 2-chromatic cases, and offers polynomial-time solutions for some 3-chromatic deficiency decision problems.

Findings

Classified deficiency for 2-chromatic signed graphs

Developed polynomial-time algorithm for maximum deficiency in 3-chromatic signed graphs

Addressed decision problems related to deficiency in signed graphs

Abstract

We introduce the concept of deficiency in signed graphs. The deficiency of a coloration is the number of unused colors. We classify the deficiency of 2-chromatic graphs. There are four decision problems about the minimum and maximum deficiency of a 3-chromatic signed graph. We answer two of them with a polynomial-time algorithm for deciding the maximum deficiency of a 3-chromatic signed graph.