Coloring decompositions of complete geometric graphs

  title={Coloring decompositions of complete geometric graphs},
  author={Clemens Huemer and Dolores Lara and Christian Rubio-Montiel},
  journal={Acta Mathematica Hungarica},
A decomposition of a non-empty simple graph $G$ is a pair $[G,P]$, such that $P$ is a set of non-empty induced subgraphs of $G$, and every edge of $G$ belongs to exactly one subgraph in $P$. The chromatic index $\chi'([G,P])$ of a decomposition $[G,P]$ is the smallest number $k$ for which there exists a $k$-coloring of the elements of $P$ in such a way that: for every element of $P$ all of its edges have the same color, and if two members of $P$ share at least one vertex, then they have… 

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