关于Weichsel猜想的一点注记(英文)

A Note on Weichsel's Conjecture

设P是n-立方体图Q_n的完备控制集．在1994年,Weichsel证明了存在某些整数r_1,r_2,…,r_m使P在Q+n中的诱导子图〈P〉为Q_(r1),Q_(r2),…,Q_(rm)的不交之并,并且猜想r_1=r_2=…=r_m．本文证明了当m≤20时,该猜想正确．

Let P be a perfect dominating set of the n-cube Qn. In 1994 Weichsel proved that the induced subgraph （P） of P in Qn is the disjoint union of copies of cubes {Qr1, Qr2,…, Qrm} for some set of integers {rl, r2,…,rm} and conjectured that r1=r2=…=rm. In this paper we show that the conjecture is true for m ≤ 20..