Vertex insertion approximates the crossing number of apex graphs
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | European Journal of Combinatorics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.ejc.2011.09.009 |
| Field | Informatics |
| Keywords | crossing number; crossing minimization; apex graph |
| Description | We show that the crossing number of an apex graph, i.e.\ a graph $G$ from which only one vertex $v$ has to be removed to make it planar, can be approximated up to a factor of $\Delta(G-v)\cdot d(v)/2$ by solving the \emph{vertex inserting} problem, i.e.\ inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm for the crossing number problem of apex graphs with bounded degree. |
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