The Extremal Function for Two Disjoint Cycles

Sufficient Condition for the Existence of Three Disjoint Theta Graphs

“…Our research is motivated by the conjecture put forward by Gao and Ji [7]. Conjecture 1.6 ( [7]). Let k ≥ 2 be an integer.…”

“…If the conjecture is true, then the bound on size is best possible, which can be seen as following examples in [7]: Let G 1 be K 1 + (K 4k−2 ∪ ⌋, because of l = 5 + ε l . By induction hypothesis, G ′ contains three disjoint theta graphs, say T 1 , T 2 and T 3 , respectively.…”