群色临界图的一些性质

Some Properties of Group Color Criticality of Graphs

群色数χ1(G)是最小数m,使得对任意Abel群A,若|A|≥m,则G是A-可着色的.称G是群色临界的,若对于G的任一真子图H,有χ1(H)<χ1(G).研究了群色临界图的一些性质,给出某些群色临界图的刻划,证明了k群色临界图G的最小度为k-1,且若G是3群色临界图当且仅当G是圈.

G is a graph, its group chromatic number χ_1(G) is the minimum number m for which G is A-colorable for any Abelian group A of order≥ m under the orientation D.G is a group color critical, if for any subgraph H of G,χ_1(H)<χ_1(G), investigate group color criticality of graphs and characterize some graphs which is group color critical, prove that the minimum degree of k group color criticality of graph is k-1,and G is 3 group color critical if and only if G is cycle.