Other formats:
BibTeX
LaTeX
RIS
@inproceedings{792439, author = {Hliněný, Petr and Chimani, Markus and Mutzel, Petra}, address = {Berlin}, booktitle = {Symposium Graph Drawing 2008, Lecture Notes in Computer Science}, doi = {http://dx.doi.org/10.1007/978-3-642-00219-9_42}, edition = {5417}, keywords = {crossing number; crossing minimization; apex graph}, howpublished = {tištěná verze "print"}, language = {eng}, location = {Berlin}, isbn = {978-3-642-00218-2}, pages = {432-434}, publisher = {Springer Verlag}, title = {Approximating the Crossing Number of Apex Graphs}, url = {http://www.gd2008.org/}, year = {2009} }
TY - JOUR ID - 792439 AU - Hliněný, Petr - Chimani, Markus - Mutzel, Petra PY - 2009 TI - Approximating the Crossing Number of Apex Graphs PB - Springer Verlag CY - Berlin SN - 9783642002182 KW - crossing number KW - crossing minimization KW - apex graph UR - http://www.gd2008.org/ L2 - http://www.gd2008.org/ N2 - 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. ER -
HLINĚNÝ, Petr, Markus CHIMANI and Petra MUTZEL. Approximating the Crossing Number of Apex Graphs. In \textit{Symposium Graph Drawing 2008, Lecture Notes in Computer Science}. 5417th ed. Berlin: Springer Verlag, 2009, p.~432-434. ISBN~978-3-642-00218-2. Available from: https://dx.doi.org/10.1007/978-3-642-00219-9\_{}42.
|