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arXiv · 2608.29101

A Chv\'atal--Erd\H{o}s type condition for supereulerian digraphs with $\alpha_{2}=4$

Zirui Liu·Jin Yan·Jia Zhou
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Abstract

A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let $\alpha_2(D)$ denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we characterize supereulerianity in a strong digraph $D$ with $\alpha_2(D)=4$ by proving that a strong digraph $D$ with $\alpha_2(D)=4$ and $\lambda(D)\ge 2$ is supereulerian if and only if $D$ does not belong to an exceptional family $\mathcal H$ of $2$-arc-strong digraphs with $\alpha_2(D)=4$. Furthermore, every strong digraph satisfying $\alpha_2(D)=4$ and $\lambda(D)\geq3$ is supereulerian.

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Zirui Liu, Jin Yan, Jia Zhou. 2026-08-29. A Chv\'atal--Erd\H{o}s type condition for supereulerian digraphs with $\alpha_{2}=4$. https://arxiv.org/abs/2608.29101

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