Defective colouring of hypergraphs
We prove that the vertices of every (r + 1)-uniform hypergraph with maximum degree ∆ may be coloured with c( ∆ d+1 ) 1/r colours such that each vertex is in at most d monochromatic edges. This result, which is best possible up to the value of the constant c, generalises the classical result of Erdos...
| Hlavní autoři: | , , , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
Wiley
2023
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| Shrnutí: | We prove that the vertices of every (r + 1)-uniform hypergraph with maximum degree ∆ may be coloured with c( ∆ d+1 ) 1/r colours such that each vertex is in at most d monochromatic edges. This result, which is best possible up to the value of the constant c, generalises the classical result of Erdos and Lov ˝ asz who proved the ´ d = 0 case. |
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