Graphs and Combinatorics

, Volume 35, Issue 1, pp 207–219 | Cite as

Snarks with Special Spanning Trees

  • Arthur Hoffmann-OstenhofEmail author
  • Thomas Jatschka
Original Paper


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.


Cubic graph Snark Spanning tree Hist 3-Edge coloring 



A.Hoffmann-Ostenhof was supported by the Austrian Science Fund (FWF) project P 26686. The computational results presented have been achieved by using the Vienna Scientific Cluster (VSC).


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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Logic and ComputationTechnische Universität WienViennaAustria

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