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PreprintCC BY 4.0arXiv

Generalized Sterboul--Deming Configurations

  • Daniel A Jaume
  • Cristian Panelo
  • Kevin Pereyra
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Abstract

Sterboul and Deming gave classical matching-based characterizations of non-Kőnig--Egerváry graphs through flower--posy and blossom-pair configurations. We consider two classical configuration families, denoted T and S, and introduce a new walk-based family J, based on J-flowers and J-posies. Our main result proves that, for every graph G, SDT(G)=SDS(G)=SDJ(G). Thus the additional flexibility of the J-framework preserves the set of vertices detected by the classical configurations. The proof is vertex-preserving and passes through strict-Hall structure in traces of J-posies. As a consequence, every prescribed vertex of a connected matchable strict-Hall graph lies in a rigid T-posy for a suitable perfect matching, linking the theory naturally with matching-covered graphs.

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Cite

BibTeXRIS
BibTeX
@misc{jaume2026generalized,
  title = {{Generalized Sterboul--Deming Configurations}},
  author = {Daniel A Jaume and Cristian Panelo and Kevin Pereyra},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12128},
  eprint = {2609.12128},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12128},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Sterboul--Deming Configurations
AU  - Daniel A Jaume
AU  - Cristian Panelo
AU  - Kevin Pereyra
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.12128
UR  - https://arxiv.org/abs/2609.12128
AB  - Sterboul and Deming gave classical matching-based characterizations of non-Kőnig--Egerváry graphs through flower--posy and blossom-pair configurations. We consider two classical configuration families, denoted T and S, and introduce a new walk-based family J, based on J-flowers and J-posies. Our main result proves that, for every graph G, SD_T(G)=SD_S(G)=SD_J(G). Thus the additional flexibility of the J-framework preserves the set of vertices detected by the classical configurations. The proof is vertex-preserving and passes through strict-Hall structure in traces of J-posies. As a consequence, every prescribed vertex of a connected matchable strict-Hall graph lies in a rigid T-posy for a suitable perfect matching, linking the theory naturally with matching-covered graphs.
ER  -