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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.27424 |
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Table of Contents:
- In this paper, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an integer linear program. Roughly speaking, a complete $S$-partite graph is obtained by replacing every single node of $S$ with a number of nodes, preserving the edge/non-edge relations of $S$. Our motivation in finding largest $2$-regular subgraphs is rooted in the structural systems theory, particularly in the problem of finding largest subnetworks that can sustain controllability or asymptotic stability of the corresponding subsystems. A main contribution of the paper is to show that the integer linear problem can be solved efficiently in $O(|V(S)|^3)$, independent of the order/size of the $S$-partite graph itself. Furthermore, we demonstrate through simulations that with high probability, a random $S$-partite graph contains a largest $2$-regular subgraph of the same order as its complete counterpart does.