Seminár z algebratickej teórie grafov - Martin Mačaj (30.11.2018)

v piatok 30.11.2018 o 13:30 hod. v miestnosti M/XI

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Prednášajúci: Martin Mačaj

Názov: On packings of disjoint copies of the Hoffman-Singleton graph into $K_{50}$

Termín: 30.11.2018, 13:30 hod., M/XI

Abstrakt:
In 1983, A.J. Schwenk asked whether it is possible to decompose $K_{10}$ into three copies of the Petersen graph. In an analogous way, we may ask whether there exists a decomposition of $K_{50}$ into seven copies of the Hoffman-Singleton graph (HoSi). Further, in a paper published in 2010, E.R. van Dam and M. Muzychuk asked whether there exists a $SRG(50,21,8,9)$ which can be decomposed into three copies of HoSi. Similarly, we may ask for a decomposition of a $SRG(50,28,15,16)$ into four copies of HoSi. Using methods of J. \v Siagiov\'a and M. Meszka, we answer these questions under the condition that all HoSis share a non-trivial automorphism.

 

 

 

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