Perfect matching cover indices of generalized rotation snarks

Wenjuan Zhou, Rong-Xia Hao and Yilun Luo

Applied Mathematics and Computation, 2025, vol. 487, issue C

Abstract: Let Γ be a 3-regular bridgeless graph and τ(Γ) be the perfect matching cover index of Γ. It is conjectured by Berge that τ(Γ)≤5. Esperet and Mazzuoccolo (2013) [4] proved that deciding whether Γ satisfies τ(Γ)≤4 is NP-complete. Máčajová and Škoviera (2021) [13] gave a family R={Rk:k≥4} of rotation snarks. We construct a family FR={FR2n+1:n≥1} of generalized rotation snarks. In this paper, we show that each FR2n+1 satisfies τ(FR2n+1)=4. As a corollary, each Rk satisfies τ(Rk)=4.

Keywords: Perfect matching cover index; Berge conjecture; Flower rotation snark (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005629

DOI: 10.1016/j.amc.2024.129101

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