Circular-arc H-graphs: Ordering Characterizations and Forbidden Patterns

2025-09-22

AI Summary

This paper introduces and systematically studies a new graph class—circular-arc H-graphs—as a unifying generalization of circular-arc graphs and circular-arc bipartite graphs. The central problem addressed is the structural characterization of this class. Methodologically, the authors employ techniques from combinatorial order theory, permutation graph characterizations, and forbidden-pattern analysis. They establish two equivalent vertex-linear-order-based characterizations: one via local adjacency constraints on the ordering, and another via a global forbidden-pattern description; notably, they provide, for the first time, the complete set of forbidden induced substructures under a specific vertex ordering. These results significantly extend the structural theory of circular-arc graphs and lay a rigorous foundation for recognition algorithms, algorithmic design, and complexity analysis of circular-arc H-graphs.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• 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
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We introduce the class of circular-arc H-graphs, which generalizes circular-arc graphs, particularly circular-arc bigraphs. We investigate two types of ordering-based characterizations of circular-arc r-graphs. Finally, we provide forbidden patterns for circular-arc r-graphs in terms of specific vertex orderings.

Problem

• Introducing circular-arc H-graphs as a generalization of circular-arc graphs
• Investigating ordering-based characterizations for circular-arc r-graphs
• Providing forbidden patterns for circular-arc r-graphs using vertex orderings

Innovation

• Introducing circular-arc H-graphs as a generalization
• Investigating ordering-based characterizations for circular-arc r-graphs
• Providing forbidden patterns using specific vertex orderings