▁ 1 9 1 7 ▁Category : Build ings ▁and ▁structures ▁in ▁As he ville , ▁North ▁Carolina ▁Category : National ▁Register ▁of ▁Historic ▁Places ▁in ▁Bun com be ▁County , ▁North ▁Carolina <0x0A> </s> ▁In ▁graph ▁theory , ▁an ▁edge ▁color ing ▁of ▁a ▁graph ▁is ▁an ▁assignment ▁of ▁" colors " ▁to ▁the ▁edges ▁of ▁the ▁graph ▁so ▁that ▁no ▁two ▁incident ▁edges ▁have ▁the ▁same ▁color . ▁ ▁For ▁example , ▁the ▁figure ▁to ▁the ▁right ▁shows ▁an ▁edge ▁color ing ▁of ▁a ▁graph ▁by ▁the ▁colors ▁red , ▁blue , ▁and ▁green . ▁Edge ▁color ings ▁are ▁one ▁of ▁several ▁different ▁types ▁of ▁graph ▁color ing . ▁The ▁edge - color ing ▁problem ▁asks ▁whether ▁it ▁is ▁possible ▁to ▁color ▁the ▁edges ▁of ▁a ▁given ▁graph ▁using ▁at ▁most ▁ ▁different ▁colors , ▁for ▁a ▁given ▁value ▁of ▁, ▁or ▁with ▁the ▁few est ▁possible ▁colors . ▁ ▁The ▁minimum ▁required ▁number ▁of ▁colors ▁for ▁the ▁edges ▁of ▁a ▁given ▁graph ▁is ▁called ▁the ▁chrom atic ▁index ▁of ▁the ▁graph . ▁ ▁For ▁example , ▁the ▁edges ▁of ▁the ▁graph ▁in ▁the ▁illustr ation ▁can ▁be ▁colored ▁by ▁three ▁colors ▁but ▁cannot ▁be ▁colored ▁by ▁two ▁colors , ▁so ▁the ▁graph ▁shown ▁has ▁chrom atic ▁index ▁three . ▁ ▁By ▁V izing ' s ▁theorem , ▁the ▁number ▁of ▁colors ▁needed ▁to ▁edge ▁color ▁a ▁simple ▁graph ▁is ▁either ▁its ▁maximum ▁degree ▁ ▁or ▁. ▁For ▁some ▁graphs , ▁such ▁as ▁b ipart ite ▁graphs ▁and ▁high - deg