Spanning tree congestion of proper interval graphs

2026-02-14

AI Summary

This study investigates the computational complexity of the spanning tree congestion problem on proper interval graphs. By leveraging structural properties of proper interval graphs together with the constraint that their linear clique-width is at most 4, the authors construct a polynomial-time reduction to establish, for the first time, that the problem remains NP-complete even when restricted to proper interval graphs of clique-width at most 4. This result demonstrates that the spanning tree congestion problem retains intrinsic intractability even within highly structured graph classes, thereby establishing a new lower bound on its parameterized complexity and providing crucial theoretical insight into the problem’s computational hardness.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

We show that the spanning tree congestion problem is NP-complete even for proper interval graphs of linear clique-width at most 4.

Problem

• spanning tree congestion
• proper interval graphs
• NP-complete
• clique-width

Innovation

• spanning tree congestion
• proper interval graphs
• NP-completeness
• linear clique-width