Extremal digraphs avoiding distinct walks of length 3 with the same endpoints |
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| Affiliation: | 1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, PR China;2. School of Science, Shenyang Aerospace University, Shenyang, 110136, PR China |
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| Abstract: | In this paper, we determine the maximum size of digraphs on n vertices which avoid two distinct walks of length 3 with the same initial vertex and the same terminal vertex. The digraphs attaining this maximum size are also characterized. Combining this with previous results, we obtain a full solution to a problem proposed by X. Zhan in 2007. |
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| Keywords: | Digraph Turán problem Walk |
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