An Algorithm for Optimal Acyclic Edge-Colouring of Cubic Graphs

@inproceedings{Mcajov2011AnAF,
  title={An Algorithm for Optimal Acyclic Edge-Colouring of Cubic Graphs},
  author={Edita M{\'a}cajov{\'a} and J{\'a}n Maz{\'a}k},
  booktitle={FAW-AAIM},
  year={2011}
}
Anacyclic edge-colouring of a graph is a proper edge-colouring such that the subgraph induced by the edges of any two colours is acyclic. The acyclic chromatic index of a graph G is the smallest possible number of colours in an acyclic edge-colouring of G. In [12], we have shown that the acyclic chromatic index of a connected subcubic graph G is at most 4 with the exception of K4 and K3,3, for which five colors are optimal. Here we give a quadratic-time algorithm that finds an acyclic 4-edge… 
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