| 完全二分图上星博弈的一个公式 |
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| 引用本文： | 张国志,王世英. 完全二分图上星博弈的一个公式[J]. 晋中学院学报, 2008, 25(3): 42-43 |
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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,数学学院,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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| 摘 要： | 给出了在完全二分图Kp,p上星博弈时一方成功数a2(K1,n)的定义:甲乙二人在完全二分图Kp,p上博弈,首先甲用绿色对Kp,p的一条边染色,接着乙用红色染Kp,p的另一条无色边,如此甲乙交替地对Kp,p的无色边进行着色.若甲在Kp,p上染成绿星K1,n,且乙在Kp,p上还没有染成红星K1,n,甲胜.否则甲负乙胜.甲能取胜的最小值p=p(n)称为K1,n的一方成功数,记成a2(K1,n).证明了a2(K1,5)=7.
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| 关 键 词： | 完全二分图 一方成功数 星博弈 |
A Formula of Star-game on Complete Bipartite Graphs |
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| ZHANG Guo-zhi,WANG Shi-ying. A Formula of Star-game on Complete Bipartite Graphs[J]. Journal of Jinzhong University, 2008, 25(3): 42-43 |
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| Authors: | ZHANG Guo-zhi WANG Shi-ying |
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| Abstract: | Unilateral successful number a2(K1,n) of the star-game on some complete bipartite graph Kp,p has been defined in this paper.Suppose Person A and B contest on a complete bipartite graph Kp,p.A first colors one of the edges of Kp,p green,B then colors another edge red.A and B color the rest edges alternately.A wins the game if what A has colored forms A star K1,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 a2(K1,n).In this paper, it is proved that a2(K1,5)=7. |
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| Keywords: | complete bipartite graph unilateral successful number star-game |
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