Seminar of Graph Theory - Martin ŠKoviera (5.3.2020)

Thursday 5.3.2020 at 9:50, Lecture room M/213

---

Martin Škoviera:
Binary snarks with rotation symmetry

Abstrakt:
A binary snark is a cubic graph which cannot be properly 3-edge-coloured and is spanned by the balanced cubic tree T_d of depth d for some d. A binary snark G is called a rotation snark if an automorphism of T_d that cyclically permutes the edges incident with the root of T_d extends to an automorphism of G. One motivation for the study of rotation snarks comes from the intention to find small snarks of girth 7 and even cyclically 7-connected snarks. So far, only very few binary snarks have been found (one of them being the Petersen graph), mostly as a result of an extensive computer search. We present a construction of infinitely many rotation snarks with cyclic connectivity 5.

This is a joint work with Edita Macajova.

 

 

---