Symmetry and the crossing number for complete 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 ...
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Let G be an abstract graph. Motivated by the Orchard relation, introduced in [3, 4], we have defined the Orchard crossing number of G [5], in a similar way to the well-known rectilinear crossing number of an abstract graph G (denoted by cr(G), see [1, 8]). A general reference for crossing numbers can be [6]. The Orchard crossing number is interesting for several reasons. First, it is based on t...
متن کاملThe Crossing Number of Seq-Shellable Drawings of Complete Graphs
The Harary-Hill conjecture states that for every n > 0 the complete graph on n vertices Kn, the minimum number of crossings over all its possible drawings equals H(n) := 1 4 ⌊n 2 ⌋⌊n− 1 2 ⌋⌊n− 2 2 ⌋⌊n− 3 2 ⌋ . So far, the lower bound of the conjecture could only be verified for arbitrary drawings of Kn with n ≤ 12. In recent years, progress has been made in verifying the conjecture for certain ...
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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 Is Hard for Cubic Graphs
It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP -hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We prove here that it is NP -hard to determine the crossing number of a simple cubic graph. In particular, this implies that the minor-monotone version of crossing number is also NP -hard, which has been...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences
سال: 1969
ISSN: 0098-8979
DOI: 10.6028/jres.073b.018