Colorings of complements of line graphs

Our purpose is to show that complements of line graphs (of graphs) enjoy nice coloring properties. We for all in this class the local and usual chromatic numbers are equal. also prove a sufficient condition number be equal natural upper bound. A consequence latter complete characterization induced subgraphs Kneser graph KG ( n , 2 ) have its number, namely − 2. In addition bound, lower bound provided by Dol'nikov's theorem, classical result topological method theory. NP-hardness deciding equality between any these bounds. The especially suitable study properties hypergraphs. Nevertheless, proofs article elementary we provide short discussion on ability methods cover some our results.