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arXiv · 2403.19312

On the $k$-anti-traceability Conjecture

Bin Chen·Stefanie Gerke·Gregory Gutin·Hui Lei·Heis Parker-Cox·Yacong Zhou
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Abstract

An oriented graph is called $k$-anti-traceable if the subdigraph induced by every subset with $k$ vertices has a hamiltonian anti-directed path. In this paper, we consider an anti-traceability conjecture. In particular, we confirm this conjecture holds when $k\leq 4$. We also show that every sufficiently large $k$-anti-traceable oriented graph admits an anti-path that contains $n-o(n)$ vertices.

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Bin Chen, Stefanie Gerke, Gregory Gutin, Hui Lei, Heis Parker-Cox, Yacong Zhou. 2024-03-28. On the $k$-anti-traceability Conjecture. https://arxiv.org/abs/2403.19312

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