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- W4210366803 abstract "Abstract A digraph is ‐ dominating if every set of at most vertices has a common out‐neighbor. For all integers , let be the smallest integer such that the vertices of every 2‐edge‐colored (finite or infinite) complete digraph (including loops) can be covered by the vertices of at most monochromatic ‐dominating subgraphs. Note that the existence of is not obvious – indeed, the question which motivated this paper was simply to determine whether is bounded, even for . We answer this question affirmatively for all , proving and . We also give an example to show that there is no analogous bound for more than two colors. Our result provides a positive answer to a question regarding an infinite analogue of the Burr‐Erdős conjecture on the Ramsey numbers of ‐degenerate graphs. Moreover, a special case of our result is related to properties of ‐paradoxical tournaments." @default.
- W4210366803 created "2022-02-08" @default.
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- W4210366803 date "2022-01-31" @default.
- W4210366803 modified "2023-09-27" @default.
- W4210366803 title "Covering 2‐colored complete digraphs by monochromatic d $d$‐dominating digraphs" @default.
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- W4210366803 doi "https://doi.org/10.1002/jgt.22804" @default.
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