## Abstract We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings. We also determine the size
Edge-Colorings of Complete Graphs that Avoid Polychromatic Trees
β Scribed by Tao Jiang; Douglas B. West
- Book ID
- 108497954
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 485 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1571-0653
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π SIMILAR VOLUMES
We prove an asymptotic existence theorem for decompositions of edge-colored complete graphs into prespecified edge-colored subgraphs. Many combinatorial design problems fall within this framework. Applications of our main theorem require calculations involving the numbers of edges of each color and
## Abstract For __k__β=β1 and __k__β=β2, we prove that the obvious necessary numerical conditions for packing __t__ pairwise edgeβdisjoint __k__βregular subgraphs of specified orders __m__~1~,__m__~2~,β¦ ,__m__~t~ in the complete graph of order __n__ are also sufficient. To do so, we present an edge