PreprintCC BY-NC-ND 4.0arXiv
Every cubic graph has four total dominating sets covering each vertex at most twice
Abstract
In 2018, Goddard and Henning conjectured that every cubic graph has four total dominating sets covering each vertex at most twice, and asked the analogous question for transversals of $3$-uniform $3$-regular hypergraphs. We prove the conjecture, which also answers the question in the affirmative.
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BibTeX
@misc{kwon2026every,
title = {{Every cubic graph has four total dominating sets covering each vertex at most twice}},
author = {Hyemin Kwon and Boram Park and Yoshio Sano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19450},
eprint = {2610.19450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19450},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Every cubic graph has four total dominating sets covering each vertex at most twice
AU - Hyemin Kwon
AU - Boram Park
AU - Yoshio Sano
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19450
UR - https://arxiv.org/abs/2610.19450
AB - In 2018, Goddard and Henning conjectured that every cubic graph has four total dominating sets covering each vertex at most twice, and asked the analogous question for transversals of $3$-uniform $3$-regular hypergraphs. We prove the conjecture, which also answers the question in the affirmative.
ER -