Improvement on the Crossing Number of Crossing-Critical Graphs
نویسندگان
چکیده
منابع مشابه
META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملCrossing Number Graphs
In 1940, the Hungarian mathematician Paul Turán was sent to a forced labor camp by the Nazis. Though every part of his life was brutally controlled, he still managed to do serious mathematics under the most extreme conditions. While forced to collect wire from former neighborhoods, he would be thinking about mathematics. When he found scraps of paper, he wrote down his theorems and conjectures....
متن کاملCrossing Number of Toroidal Graphs
It is shown that if a graph of n vertices can be drawn on the torus without edge crossings and the maximum degree of its vertices is at most d, then its planar crossing number cannot exceed cdn, where c is a constant. This bound, conjectured by Brass, cannot be improved, apart from the value of the constant. We strengthen and generalize this result to the case when the graph has a crossing-free...
متن کاملInfinite families of crossing-critical graphs with prescribed average degree and crossing number
iráň constructed infinite families of k-crossing-critical graphs for every k ≥ 3 and Kochol constructed such families of simple graphs for every k ≥ 2. Richter and Thomassen argued that, for any given k ≥ 1 and r ≥ 6, there are only finitely many simple k-crossingcritical graphs with minimum degree r. Salazar observed that the same argument implies such a conclusion for simple k-crossing-critic...
متن کاملCrossing and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G− e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from different combinatorial viewpoints. On the one hand, we develop min-max formulas involving efficiently computable lower and upper bounds. These min-max results are the first of their kind in the study of crossing numbers an...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2020
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-020-00264-2