arXiv subjects

Thomas Jatschka

Publications and source records attributed to Thomas Jatschka.

2 recordsLinked to original sources

arXiv2018

Snarks with special spanning trees

Let $G$ be a cubic graph which has a decomposition into a spanning tree $T$ and a $2$-regular subgraph $C$, i.e. $E(T) \cup E(C) = E(G)$ and $E(T) \cap E(C) = \emptyset$. We provide an answer to the following question: which lengths can the cycles of $C$ have if $G$ is a snark? Note that $T$ is a hist (i.e. a spanning tree without a vertex of degree two) and that every cubic graph with a hist has the above decomposition.

math.CO↗

arXiv2017

Special Hist-Snarks

A Hist in a cubic graph $G$ is a spanning tree $T$ which has only vertices of degree three and one. A snark with a Hist is called a Hist-snark, see \cite{HO}. We present several computer generated Hist-snarks which form generalizations of the Petersen graph. Moreover, we state some results on Hist-snarks which have been achieved with computer support.

math.CO↗