A. Hoffmann-Ostenhof, T. Jatschka:

"Snarks with Special Spanning Trees";

Graphs and Combinatorics,1(2018), 1 - 13.

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)∪E(C)=E(G) and E(T)∩E(C)=∅. 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.

Cubic graph; Snark Spanning tree; Hist 3-Edge coloring

http://dx.doi.org/10.1007/s00373-018-1973-x

https://publik.tuwien.ac.at/files/publik_273966.pdf

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