| 一方成功数a(K1,4)等于7 |
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| 引用本文： | 张国志,王世英.一方成功数a(K1,4)等于7[J].中北大学学报,2006,27(2):156-159. |
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| 作者姓名： | 张国志 王世英 |
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| 作者单位： | [1]晋中学院数学系,山西晋中030600 [2]山西大学数学科学学院,山西太原030006 |
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| 基金项目： | 山西省自然科学基金
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中国科学院资助项目 |
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| 摘 要： | 给出了一方成功数a(K1,n)的新定义:甲乙二人在完全图Kp上博弈,首先甲用绿色把Kp的一条边上色,接着乙用红色染Kp的另一条无色边,如此甲乙交替地对Kp的无色边进行着色,若甲在Kp上染成绿星K1,n且乙在Kp上没有染成红星K1,n,甲赢;否则甲输乙赢.甲能取胜的最小值p=p(n)称为K1,n的一方成功数,记成a(K1,n).应用穷举法,本文获得了一方成功数a(K1,4)=7.
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| 关 键 词： | 一方成功数 星博弈 完全图 |
| 文章编号： | 1673-3193(2006)02-0156-04 |
| 修稿时间： | 2005年10月29 |
Unilateral Successful Number a(K1,4) Being 7 |
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| ZHANG Guo-zhi,WANG Shi-ying.Unilateral Successful Number a(K1,4) Being 7[J].Journal of North University of China,2006,27(2):156-159. |
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| Authors: | ZHANG Guo-zhi WANG Shi-ying |
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| Abstract: | Unilateral successful number a(K_1,n) has been redefined in this paper: Suppose person a and b contest on complete graph K_p.a first colors one of the edges of K_p green,b then colors another edge red.a and b color the rest edge alternately.a wins the game if what a has colored forms a star K_1,n while b fails to.The smallest natural number P=P(n) for a to win the game is called the unilateral successful number,denoted a(K_1,n).The authors have proved that a(K_1,4) equals 7 by using exhaustive method. |
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| Keywords: | unilateral successful number star game complete graph |
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