| Autor: |
Chen, G., Fujita, S., Gyarfas, A., Lehel, J., Toth, A. |
| Rok vydání: |
2012 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We address an old (1977) conjecture of a subset of the authors (a variant of Ryser's conjecture): in every r-coloring of the edges of a biclique [A,B] (complete bipartite graph), the vertex set can be covered by the vertices of at most 2r-2 monochromatic connected components. We reduce this conjecture to design-like conjectures, where the monochromatic components of the color classes are bicliques [X,Y] with nonempty blocks X and Y. We prove this conjecture for r<6. We show that the width (the number of bicliques) in every color class of any spanning r-coloring is at most 2^{r-1} (and this is best possible). |
| Databáze: |
arXiv |
| Externí odkaz: |
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