简介:Itisprovedthatisa(Δ+1)-colorablegraph,soarethegraphsG×PnandC×Cn,wherePnandCnarerespectivelythepathandcyclewithnvertices,andΔthemaximumedgedegreeofthegraph.TheexactchromaticnumbersoftheproductgraphsPr1×Pr2×…×PrnandC3k×C2m1×C2m2×…×C2mnarealsopresented.Thusthetltalcoloringconjectureisprovedtobetrueformanyothergraphs.