Work

On the $k$-anti-traceability Conjecture

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2403.19312

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

Institutions: Royal Holloway University of London, Nankai University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4393335934

Cites:

Cited by:

Related to: 10