岳為君, 黃元秋, 唐 玲

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岳為君1, 黃元秋*1, 唐 玲2

(1. 湖南師范大學(xué) 數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院, 湖南 長(zhǎng)沙, 410081; 2. 中南林業(yè)科技大學(xué) 理學(xué)院, 湖南 長(zhǎng)沙, 410004 )

畫法; 交叉數(shù); 聯(lián)圖; 圈

圖1 圖

1 基本性質(zhì)和引理

在證明本文的主要結(jié)果之前, 先給出一些基本性質(zhì)和引理.

首先, 由交叉數(shù)的定義, 易有如下性質(zhì):

2 定理的證明

定理1(1)的證明

定理1(2)的證明

定理1(3)的證明

圖3 的一個(gè)好畫法

以下證明總能得到一個(gè)與(1)式相矛盾的結(jié)論, 從而完成定理1(3)的證明.

根據(jù)性質(zhì)1和斷言1可得:

圖4 情形2

圖5 子情形3.1

圖6 子情形3.2

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YUE Wei-jun1, HUANG Yuan-qiu1, TANG Ling2

(1. Department of Mathematics, Hunan Normal University, Changsha 410081, China; 2. Department of Mathematics, Central South University of Forestry and Technology, Changsha 410004, China)

drawing; crossing number; join graph; cycle

10.3969/j.issn.1672-6146.2013.04.001

O 157.5

1672-6146(2013)04-0001-07

email: hyqq@hunnu.edu.cn.

email: yueweijun121@163.com.

2013-08-11

國(guó)家自然科學(xué)基金資助項(xiàng)目(11371133)

(責(zé)任編校:劉曉霞)