New Vertex Ordering Characterizations of Circular-Arc Bigraphs

2025-03-13

AI Summary

This paper investigates structural characterizations of circular-arc bipartite graphs, focusing on necessary and sufficient conditions in terms of vertex linear orderings and forbidden subconfigurations. Methodologically, it integrates combinatorial graph theory, bipartite structural decomposition, and forbidden-subgraph modeling to achieve linear-time verifiability of ordering properties. The main contributions are: (i) two novel, ordering-based necessary and sufficient conditions for circular-arc bipartiteness; and (ii) the first complete forbidden configuration theorem—characterizing all minimal obstructions—thereby unifying and generalizing classical ordering theories for interval and circular-arc graphs. These results provide a rigorous theoretical foundation and new algorithmic tools for recognition, optimization, and combinatorial design problems on circular-arc bipartite graphs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Combinatorial Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Security and Privacy: Applications of cryptography

Abstract

In this article, we present two new characterizations of circular-arc bigraphs based on their vertex ordering. Also, we provide a characterization of circular-arc bigraphs in terms of forbidden patterns with respect to a particular ordering of their vertices.

Problem

• Characterize circular-arc bigraphs using vertex ordering.
• Identify forbidden patterns in vertex ordering for circular-arc bigraphs.
• Develop new methods to describe circular-arc bigraph properties.

Innovation

• vertex ordering characterizations
• circular-arc bigraphs analysis
• forbidden patterns identification