The edge intersection graphs of paths in a tree

@article{Golumbic1985TheEI,
  title={The edge intersection graphs of paths in a tree},
  author={Martin Charles Golumbic and Robert E. Jamison},
  journal={J. Comb. Theory, Ser. B},
  year={1985},
  volume={38},
  pages={8-22}
}
The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) is investigated, where two paths edge intersect if they share an edge. The cliques of an EPT graph are characterized and shown to have strong Helly number 4. From this it is demonstrated that the problem of finding a maximum clique of an EPT graph can be solved in polynomial time. It is shown that the strong perfect graph conjecture holds for EPT graphs. Further complexity results follow from the observation… CONTINUE READING
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