The Crossing Number of K 11 is 100 January 29 , 2007
نویسندگان
چکیده
The crossing number of Kn is known for n 6 10. We develop several simple counting properties that we shall exploit in showing by computer that cr(K11) = 100, which implies that cr(K12) = 150. We also determine the numbers of non-isomorphic optimal drawings of K9 and K10.
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 کاملNew Lower Bounds for the Number of (<=k)-Edges and the Rectilinear Crossing Number of Kn
We provide a new lower bound on the number of (≤ k)-edges of a set of n points in the plane in general position. We show that for 0 ≤ k ≤ bn−2 2 c the number of (≤ k)-edges is at least Ek(S) ≥ 3 ( k + 2 2 ) + k ∑ j=b3 c (3j − n + 3), which, for b3 c ≤ k ≤ 0.4864n, improves the previous best lower bound in [11]. As a main consequence, we obtain a new lower bound on the rectilinear crossing numbe...
متن کاملImplementation of a Clinical Pharmacy Education Program in a Teaching Hospital: Resident Oriented Documentation and Intervention
The aim of this study was to provide a clinical pharmacy education program at Masih Daneshvari hospital, a University affiliated hospital, located in Tehran, Iran. For this purpose, the most common pharmacist involved interventions and aspects of potential fields for pharmacy students and residents education was firstly identified. Clinical pharmacy interventions and drug information forms wer...
متن کاملImplementation of a Clinical Pharmacy Education Program in a Teaching Hospital: Resident Oriented Documentation and Intervention
The aim of this study was to provide a clinical pharmacy education program at Masih Daneshvari hospital, a University affiliated hospital, located in Tehran, Iran. For this purpose, the most common pharmacist involved interventions and aspects of potential fields for pharmacy students and residents education was firstly identified. Clinical pharmacy interventions and drug information forms wer...
متن کاملNote on the Pair-Crossing Number and the Odd-Crossing Number
The crossing number cr(G) of a graph G is the minimum possible number of edge-crossings in a drawing of G, the pair-crossing number pcr(G) is the minimum possible number of crossing pairs of edges in a drawing of G, and the odd-crossing number ocr(G) is the minimum number of pairs of edges that cross an odd number of times. Clearly, ocr(G) ≤ pcr(G) ≤ cr(G). We construct graphs with 0.855 · pcr(...
متن کامل