AbstractLet $$S=K[x_1,\ldots ,x_n]$$ S = K [ x 1 , … , x n ] , where K is a field, and $$t_i(S/I)$$ t i ( S / I ) denotes the maximal shift in the minimal graded free S-resolution of the graded algebra S/I at degree i, where I is an edge ideal. In this paper, we prove that if $$t_b(S/I)\ge \lceil \frac{3b}{2} \rceil $$ t b ( S / I ) ≥ ⌈ 3 b 2 ⌉ for some $$b\ge 0$$ b ≥ 0 , then the subadditivity condition $$t_{a+b}(S/I)\le t_a(S/I)+t_b(S/I)$$ t a + b ( S / I ) ≤ t a ( S / I ) + t b ( S / I ) holds for all $$a\ge 0$$ a ≥ 0 . In addition, we prove that $$t_{a+4}(S/I)\le t_a(S/I)+t_4(S/I)$$ t a + 4 ( S / I ) ≤ t a ( S / I ) + t 4 ( S / I ) for all $$a\ge 0$$ a ≥ 0 (the case $$b=0,1,2,3$$ b = 0 , 1 , 2 , 3 is known). We conclude that if the projective dimension of S/I is at most 9, then I satisfies the subadditivity condition.