Geodesic
Hamilton cycles in primitive graphs of order 2rs
Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article no. 05, 24 p.

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After long term efforts, it was recently proved by Du, Kutnar and Marušič in 2021 that except for the Petersen graph, every connected vertex-transitive graph of order rs has a Hamilton cycle, where r and s are primes. A natural topic is to solve the hamiltonian problem for connected vertex-transitive graphs of 2rs. This topic is quite nontrivial, as the problem is still unsolved even for that of r = 5. In this paper, it is shown that except for the Coxeter graph, every connected vertex-transitive graph of order 2rs contains a Hamilton cycle, provided the automorphism group acts primitively on vertices.
DOI : 10.26493/1855-3974.2930.8e4
Keywords: Vertex-transitive graph, Hamilton cycle, primitive group, automorphism group, orbital graph 
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Shaofei Du; Yao Tian; Hao Yu. Hamilton cycles in primitive graphs of order 2rs. Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article  no. 05, 24 p. doi : 10.26493/1855-3974.2930.8e4. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2930.8e4/

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