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A Chvátal--Erdős type condition for supereulerian digraphs with α2=4

  • Zirui Liu
  • Jin Yan
  • Jia Zhou
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Abstract

A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let α2(D) denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we characterize supereulerianity in a strong digraph D with α2(D)=4 by proving that a strong digraph D with α2(D)=4 and λ(D)≥ 2 is supereulerian if and only if D does not belong to an exceptional family ℋ of $2$-arc-strong digraphs with α2(D)=4. Furthermore, every strong digraph satisfying α2(D)=4 and λ(D)≥3 is supereulerian.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026chvátalerdős,
  title = {{A Chvátal--Erdős type condition for supereulerian digraphs with $α_2=4$}},
  author = {Zirui Liu and Jin Yan and Jia Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29101},
  eprint = {2608.29101},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29101},
}
RIS
TY  - UNPB
TI  - A Chvátal--Erdős type condition for supereulerian digraphs with α_2=4
AU  - Zirui Liu
AU  - Jin Yan
AU  - Jia Zhou
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29101
UR  - https://arxiv.org/abs/2608.29101
AB  - A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let α_2(D) denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we characterize supereulerianity in a strong digraph D with α_2(D)=4 by proving that a strong digraph D with α_2(D)=4 and λ(D)≥ 2 is supereulerian if and only if D does not belong to an exceptional family ℋ of $2$-arc-strong digraphs with α_2(D)=4. Furthermore, every strong digraph satisfying α_2(D)=4 and λ(D)≥3 is supereulerian.
ER  -