Geodesic
Permutation snarks of order 2 (mod 8)
Edita Máčajová1 ; Martin Škoviera1 ; Edita Máčajová ; Martin Škoviera
1Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 929-934 
Edita Máčajová; Martin Škoviera; Edita Máčajová; Martin Škoviera. Permutation snarks of order 2 (mod 8). Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 929-934. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a88/
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     title = { Permutation snarks of order 2 (mod 8)},
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Voir la notice de l'article provenant de la source Comenius University

A permutation snark is a cubic graph which has a 2-factor consisting oftwo chordless cycles and is not 3-edge-colourable. Every permutation snark is cyclically4-edge-connected, has girth at least 5, and its order is twice an odd number.Employing exhaustive computer search, Brinkmann et al. (2013) discovered a cyclically5-edge-connected permutation snark of order 34, disproving a conjecture ofC.-Q. Zhang (1997) that the Petersen graph is the only such graph. Hagglund andHomann-Ostenhof (2017) extended this example to an innite series of cyclically5-edge-connected permutation snarks of order n = 24k + 10 for every positive integerk. Here we present three general methods of constructing permutation snarksand with their help provide permutation snarks with cyclic connectivity 4 and 5 forevery possible order 2 (mod 8).