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Snarks with special spanning trees

2017/06/18 by Hoffmann-Ostenhof, Arthur, Jatschka, Thomas
#05Cxx #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.05595

Abstract

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.

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