一方成功数a(K_(1,4))等于7

Unilateral Successful Number a(K_(1,4)) Being 7

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.

Unilateral successful number a（K1,n） has been redefined in this paper： Suppose person a and b contest on complete graph Kp. a first colors one of the edges of Kp 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 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 α（K1,4）. The authors have proved that a（K1.4） equals 7 by using exhaustive method.