科研之友
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摘要
For r %26gt;= 2, a %26gt;= r- 1 and k %26gt;= 1, let c(r,, a, k) be the smallest integer c such that the vertex set of any non-trivial r-uniform k-edge-colored hypergraph 9-1 with = a can be covered by c monochromatic connected components. Here a(9-1) is the maximum cardinality of a subset A of vertices in 9-1 such that A does not contain any edges. An old conjecture of Ryser is equivalent to c(2, k) = a(r 1) and a recent result of Z. Kiraly states that c(r,, r-1, k) = [k/r] for any r %26gt;= 3. Here we make the first step to treat non-complete hypergraphs, showing that c(r,, r, r) = 2 for r %26gt;= 2 and c(r,, r, r+1) = 3 for r %26gt;= 3.
- 出版日期2014-5-13
