图的因子控制

Factor Domination in Graphs

P.Dankelmann和R.C.Laskar(2003年)提出如下猜想:设F1和F2是完全图Kn的两个边不交的因子,如果δ(Fi)≥2,i=1,2,则因子控制数γ(F1,F2)≤3n5。如果F1∪F2有长的交错路,则猜想成立。

P. Dankelmann and R.C. Laskar (in 2003) gave the following conjecture: Let F_1 and F_2 be edge disjoint factors of the complete graph K_n, if δ(F_1)≥2,i=1,2, then γ(F_1,F_2)≤3n5. In this paper, we prove that the conjecture holds if F_1∪F_2 contains the long alternating path.