Constructive Characterization for Signed Analogue of Critical Graphs II: General Radials and Semiradials

TL;DR

This paper extends previous work by providing a constructive characterization of general radials and semiradials, which are signed analogues of critical graphs, broadening understanding of their structure.

Contribution

It offers a new constructive characterization for general radials and semiradials, building on prior classifications of specific subclasses.

Findings

Provided a constructive characterization of general radials.

Extended the classification to include semiradials.

Connected radials and semiradials to critical graph analogues.

Abstract

This paper is a sequel of our preceding paper (N. Kita: Constructive characterization for signed analogue of critical graphs I: Principal classes of radials and semiradials. arXiv preprint, arXiv:2001.00083, 2019). In the preceding paper, the concepts of radials and semiradials are introduced, and constructive characterizations for five principal classes of radials and semiradials are provided. Radials are a common analogue of critical graphs from matching theory and a class of directed graphs called flowgraphs, whereas semiradials are a relaxed concept of radials. Five classes of radials and semiradials, that is, absolute semiradials, strong and almost strong radials, linear semiradials, and sublinear radials, were defined and characterized in the paper. In this paper, we use these characterizations to provide a constructive characterization of general radials and semiradials.