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PreprintCC BY 4.0arXiv

The Erdős-Hajnal Property for the six-vertex Graph with Edge Set {ab,bc,cd,de,af,bf,df}

Abstract

We prove that the six-vertex graph with edge set {ab,bc,cd,de,af,bf,df} has the Erdős-Hajnal property. The proof adapts the iterative-sparsification method of Nguyen, Scott, and Seymour within the comb-based framework of Huang, Ju, and Zhou.

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BibTeX
@misc{tran2026erdőshajnal,
  title = {{The Erdős-Hajnal Property for the six-vertex Graph with Edge Set $\ab,bc,cd,de,af,bf,df\$}},
  author = {Viet-Hoang Tran and Tan M. Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.28551},
  eprint = {2608.28551},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.28551},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Erdős-Hajnal Property for the six-vertex Graph with Edge Set {ab,bc,cd,de,af,bf,df}
AU  - Viet-Hoang Tran
AU  - Tan M. Nguyen
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.28551
UR  - https://arxiv.org/abs/2608.28551
AB  - We prove that the six-vertex graph with edge set {ab,bc,cd,de,af,bf,df} has the Erdős-Hajnal property. The proof adapts the iterative-sparsification method of Nguyen, Scott, and Seymour within the comb-based framework of Huang, Ju, and Zhou.
ER  -