典型文献
A Contribution to Guy's Conjecture
文献摘要：
Let Kn denote the complete graph consisting of n vertices,every pair of which forms an edge.We want to know the least possible number of the intersections,when we draw the graph Kn on the plane or on the sphere using continuous arcs for edges.In a paper published in 1960,Richard K.Guy conjectured that the least possible number of the intersections is 1/64(n-1)2(n-3)2 if n is odd,or 1/64n(n-2)2(n-4)if n is even.A virgin road Vn is a drawing of a Hamiltonian cycle in Kn consisting of n vertices and n edges such that no other edge-representing arcs cross Vn.A drawing of Kn is called virginal if it contains a virgin road.All drawings considered in this paper will be virginal with respect to a fixed virgin road Vn.We will present a certain drawing of a subgraph of Kn,for each n(≥5),which is"characteristic"in the sense that any minimal virginal drawing of Kn containing this subdrawing satisfies Guy's conjecture.
文献关键词：
中图分类号：
作者姓名：
Yukio MATSUMOTO;Yoshikazu MATSUTANI;Angel MONTESINOS-AMILIBIA;Masami ODA;Shuichi OHKI;Tsuyoshi SAKAI;Tsukasa SHIBUYA
作者机构：
Department of Mathematics,Gakushuin University,Mejiro,Toshima-ku,Tokyo 171-8588,Japan;3-21-1-901 Minamimachi,Kokubunji,Tokyo 185-0021,Japan;Calle Río Alberche,8.05260 Cebreros,Spain;Tsuda University,2-1-1,Tsuda-cho,Kodaira,Tokyo 187-8577,Japan;Tokyo Japanese Language Educational Center,3-22-7,Kita Shinjuku,Shinjuku-ku,Tokyo 169-0074,Japan;Department of Mathematics,College of Humanities and Sciences,Nihon University,Setagaya-ku,Tokyo 156-0045,Japan;YNkai,Kuriharagakuen Group,15-38-201,Saneicho,Shinjuku-ku,Tokyo 160-0008,Japan
文献出处：
引用格式：
[1]Yukio MATSUMOTO;Yoshikazu MATSUTANI;Angel MONTESINOS-AMILIBIA;Masami ODA;Shuichi OHKI;Tsuyoshi SAKAI;Tsukasa SHIBUYA-.A Contribution to Guy's Conjecture)[J].数学学报（英文版）,2022(10):1856-1886
A类：
Conjecture,64n,virginal,subdrawing
B类：
Contribution,Guy,Let,Kn,denote,complete,consisting,vertices,every,pair,which,forms,We,want,know,least,possible,number,intersections,when,we,plane,sphere,using,continuous,arcs,edges,In,paper,published,Richard,conjectured,that,if,odd,even,road,Vn,Hamiltonian,cycle,such,other,representing,cross,called,contains,All,drawings,considered,this,will,respect,fixed,certain,subgraph,each,characteristic,sense,any,minimal,containing,satisfies
AB值：
0.435211
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