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This result is used in some of our other papers on edge colorings of K2n. ... We prove that any edge-coloring of L using 2n − 1 colors can be extended to a proper edge-coloring of K 2n using the same set of colors. ... Let S be a spanning star of K 2n−1 ; where n¿4; and let be a partial total coloring of K 2n−1 such that all the edges of S receive distinct colors and all the vertices of S receive distinct colors. ...doi:10.1016/s0012-365x(99)00290-3 fatcat:7z3q56ncobhbhboy3cdtueytw4
Our aim has been to present what we consider to be the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. ... Appendix I11 includes a selection of interesting graphs with special properties. These may prove to be useful in testing new conjectures. ... one spanning tree T, then G = T. 2.2.4 Let F be a maximal forest of G . ...doi:10.2307/3008805 fatcat:plgnmnhvpbdzze5sxwmgubxgae