, ▁but ▁any ▁edge ▁present ▁in ▁both ▁graphs ▁must ▁be ▁represented ▁by ▁the ▁same ▁curve ▁in ▁both ▁draw ings . ▁The ▁classification ▁of ▁different ▁types ▁of ▁input ▁as ▁always ▁having ▁an ▁embedding ▁or ▁as ▁sometimes ▁not ▁being ▁possible ▁depends ▁not ▁only ▁on ▁the ▁two ▁types ▁of ▁graphs ▁to ▁be ▁drawn , ▁but ▁also ▁on ▁the ▁structure ▁of ▁their ▁intersection . ▁For ▁instance , ▁it ▁is ▁always ▁possible ▁to ▁find ▁such ▁an ▁embedding ▁when ▁both ▁of ▁the ▁two ▁given ▁graphs ▁are ▁outer plan ar ▁graphs ▁and ▁their ▁intersection ▁is ▁a ▁linear ▁forest , ▁with ▁at ▁most ▁one ▁b end ▁per ▁edge ▁and ▁with ▁vertex ▁coordinates ▁and ▁b end ▁points ▁all ▁belonging ▁to ▁a ▁grid ▁of ▁polynomial ▁area . ▁However , ▁there ▁exist ▁other ▁pairs ▁of ▁outer plan ar ▁graphs ▁with ▁more ▁complex ▁inter sections ▁that ▁have ▁no ▁such ▁embedding . ▁It ▁is ▁also ▁possible ▁to ▁find ▁a ▁simultane ous ▁embedding ▁with ▁fixed ▁edges ▁for ▁any ▁pair ▁of ▁a ▁plan ar ▁graph ▁and ▁a ▁tree . ▁ ▁It ▁is ▁an ▁open ▁question ▁whether ▁the ▁existence ▁of ▁a ▁simultane ous ▁embedding ▁with ▁fixed ▁edges ▁for ▁two ▁given ▁graphs ▁can ▁be ▁tested ▁in ▁polynomial ▁time . ▁However , ▁for ▁three ▁or ▁more ▁graphs , ▁the ▁problem ▁is ▁N P - complete . ▁When ▁simultane ous ▁embed d ings ▁with ▁fixed ▁edges ▁do ▁exist , ▁they ▁can ▁be ▁found ▁in ▁polynomial ▁time ▁for ▁pairs ▁of ▁outer plan ar ▁graphs , ▁and ▁for ▁B icon ne cted ▁graphs , ▁i . e . ▁pairs ▁of ▁graphs ▁whose ▁intersection ▁is