DeVos–Mohar–Samal conjecture on crossing-free drawings of disconnected graphs

Let GG be the disjoint union of two connected graphs HH and KK, and let Σ\Sigma be a surface. An optimal drawing of GG on Σ\Sigma is a drawing whose crossing number equals the crossing number of GG on Σ\Sigma.

DeVos–Mohar–Samal conjecture. For every optimal drawing of GG on Σ\Sigma, the restrictions to HH and KK do not intersect.

This conjecture concerns whether the connected components of a disconnected graph can always be drawn separately in an optimal drawing on any surface. Its status is not resolved by the supplied source context.

Sources & referencesView supporting material

Primary source

Laurent Beaudou, Antoine Gerbaud, Roland Grappe and Frederic Palesi, “Drawing disconnected graphs on the Klein bottle”, arXiv:0810.0508 (2008).

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