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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
Given a positive integer n and a family F of graphs, let R(n,F) denote the maximum number of colors in an edge-coloring of complete graph such that no subgraph of complete graph belonging to F has distinct colors on its edges. In this paper, we obtain bounds on single tree , where the single tree with s+t edges obtained by identifying a leaf of star with an endpoint of path .