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.
Related
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 -