Partial Cubes and Crossing Graphs

@article{Klavzar2002PartialCA,
  title={Partial Cubes and Crossing Graphs},
  author={Sandi Klavzar and Henry Martyn Mulder},
  journal={SIAM J. Discrete Math.},
  year={2002},
  volume={15},
  pages={235-251}
}
Partial cubes are defined as isometric subgraphs of hypercubes. For a partial cube G, its crossing graph G# is introduced as the graph whose vertices are the equivalence classes of the Djoković–Winkler relation Θ, two vertices being adjacent if they cross on a common cycle. It is shown that every graph is the crossing graph of some median graph and that a partial cube G is 2-connected if and only if G# is connected. A partial cube G has a triangle-free crossing graph if and only if G is a cube… CONTINUE READING

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