On the $k$-anti-traceability Conjecture

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

On the $k$-anti-traceability Conjecture

Combinatorics 2024-03-29 v1

Authors: Bin Chen , Stefanie Gerke , Gregory Gutin , Hui Lei , Heis Parker-Cox , Yacong Zhou

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.

Keywords

graph theory hadwiger conjecture

Cite

@article{arxiv.2403.19312,
  title  = {On the $k$-anti-traceability Conjecture},
  author = {Bin Chen and Stefanie Gerke and Gregory Gutin and Hui Lei and Heis Parker-Cox and Yacong Zhou},
  journal= {arXiv preprint arXiv:2403.19312},
  year   = {2024}
}

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15 pages, 1 figure

On the $k$-anti-traceability Conjecture

Abstract

Keywords

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