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Finding a Maximum Restricted t-Matching via Boolean Edge-CSP

Authors Yuni Iwamasa , Yusuke Kobayashi , Kenjiro Takazawa

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Author Details

Yuni Iwamasa
  • Kyoto University, Japan
Yusuke Kobayashi
  • Kyoto University, Japan
Kenjiro Takazawa
  • Hosei University, Japan

Funding

This work was partially supported by JSPS KAKENHI Grant Numbers JP20K11692, JP20K11699, JP22H05001, JP22K17854, JP24K02901, JP24K14828, and by JST ERATO Grant Number JPMJER2310.

Acknowledgements

The authors thank anonymous reviewers for their valuable comments.

Cite AsGet BibTex

Yuni Iwamasa, Yusuke Kobayashi, and Kenjiro Takazawa. Finding a Maximum Restricted t-Matching via Boolean Edge-CSP. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.75

Abstract

The problem of finding a maximum 2-matching without short cycles has received significant attention due to its relevance to the Hamilton cycle problem. This problem is generalized to finding a maximum t-matching which excludes specified complete t-partite subgraphs, where t is a fixed positive integer. The polynomial solvability of this generalized problem remains an open question. In this paper, we present polynomial-time algorithms for the following two cases of this problem: in the first case the forbidden complete t-partite subgraphs are edge-disjoint; and in the second case the maximum degree of the input graph is at most 2t-1. Our result for the first case extends the previous work of Nam (1994) showing the polynomial solvability of the problem of finding a maximum 2-matching without cycles of length four, where the cycles of length four are vertex-disjoint. The second result expands upon the works of Bérczi and Végh (2010) and Kobayashi and Yin (2012), which focused on graphs with maximum degree at most t+1. Our algorithms are obtained from exploiting the discrete structure of restricted t-matchings and employing an algorithm for the Boolean edge-CSP.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
  • Theory of computation → Discrete optimization
Keywords
  • Polynomial algorithm
  • C_k-free 2-matching
  • Jump system
  • Boolean edge-CSP

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