相关论文: Really Straight Graph Drawings
This paper has been withdrawn by the authors. There was an erroneous estimate of the degree of a transformed polynomial, making the method appear more effective than it really is. We thank an anonymous referee for pointing out this error.
This paper is being withdrawn by the authors in order to correct some errors and also to introduce improved theoretical techniques.
We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected…
This paper has been withdrawn by the author
This paper has been withdrawn. It will be split into two separate papers. New results will be added in both papers.
This paper has been withdrawn by the author, due to an error in Proposition 2.2.
This paper has been withdrawn by the author due to a crucial error in equation (51).
This paper has been withdrawn.
This paper has been withdrawn.
This paper was withdrawn by the authors because it has been supplanted by gr-qc/0311007 and gr-qc/0311038.
This paper was withdrawn. It has been superseded by the latest version of hep-th/0107069.
%auto-ignore This paper has been withdrawn by the author, due to a crucial error.
This paper has been withdrawn by the author due to an error in the derivation.
This manuscript has been withdrawn by the author. Some of the material has been included in the manuscript 'Dualizing the Dual Standard Model' hep-ph/0102084.
This paper has been withdrawn, as it should not have been a new submission. Please instead see the latest version of arXiv:0904.0436.
This paper has been withdrawn by the author.
A straight-line drawing $\delta$ of a planar graph $G$ need not be plane, but can be made so by moving some of the vertices. Let shift$(G,\delta)$ denote the minimum number of vertices that need to be moved to turn $\delta$ into a plane…
This article has been removed. It has been superseded by gr-qc/0506097.
This paper has been withdrawn by the authors due to the paper is far from complishment.
This paper has been withdrawn by the author, since most of the results have been published before.