cement ▁for ▁two ▁graphs ▁provides ▁a ▁simultane ous ▁embedding ▁of ▁the ▁two ▁graphs . ▁Research ▁has ▁concentr ated ▁on ▁finding ▁draw ings ▁with ▁few ▁b ends , ▁or ▁with ▁few ▁cross ings ▁between ▁edges ▁from ▁the ▁two ▁graphs . ▁ ▁There ▁are ▁two ▁restricted ▁models : ▁simultane ous ▁geometric ▁embedding ▁and ▁simultane ous ▁embedding ▁with ▁fixed ▁edges , ▁where ▁curves ▁or ▁b ends ▁are ▁allowed ▁in ▁the ▁edges , ▁but ▁any ▁edge ▁ ▁present ▁in ▁both ▁graphs ▁must ▁be ▁represented ▁by ▁the ▁same ▁curve ▁in ▁both ▁draw ings . ▁When ▁a ▁simultane ous ▁geometric ▁embedding ▁exists , ▁it ▁automatically ▁is ▁also ▁a ▁simultane ous ▁embedding ▁with ▁fixed ▁edges . ▁ ▁For ▁simultane ous ▁embedding ▁problems ▁on ▁more ▁than ▁two ▁graphs , ▁it ▁is ▁standard ▁to ▁assume ▁that ▁all ▁pairs ▁of ▁input ▁graphs ▁have ▁the ▁same ▁intersection ▁as ▁each ▁other ; ▁that ▁is , ▁the ▁edge ▁and ▁vertex ▁sets ▁of ▁the ▁graphs ▁form ▁a ▁sun flow er . ▁This ▁constraint ▁is ▁known ▁as ▁sun flow er ▁intersection . ▁ ▁Sim ult aneous ▁embedding ▁is ▁closely ▁related ▁to ▁thick ness , ▁the ▁minimum ▁number ▁of ▁plan ar ▁sub graph s ▁that ▁can ▁cover ▁all ▁of ▁the ▁edges ▁of ▁a ▁given ▁graph , ▁and ▁geometric ▁thick ness , ▁the ▁minimum ▁number ▁of ▁edge ▁colors ▁needed ▁in ▁a ▁straight - line ▁drawing ▁of ▁a ▁given ▁graph ▁with ▁no ▁crossing ▁between ▁same - color ed ▁edges . ▁In ▁particular , ▁the ▁thick ness ▁of ▁a ▁given ▁graph ▁is ▁two , ▁if ▁the ▁graph ' s ▁edges ▁can ▁be