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| SEYMOUR'S SECOND NEIGHBORHOOD IN 3-FREE DIGRAPHS |
| Bin Chen,An Chang |
| (Center for Discrete Math. and Theoretical Computer Science, Fuzhou University, Fuzhou 350108, Fujian, PR China) |
| DOI： |
| Abstract: |
| In this paper, we consider Seymour's Second Neighborhood Conjecture in $3$-free digraphs, and prove that for any $3$-free digraph $D$, there exists a vertex say $v$, such that $d^{++}(v)\geq \lfloor\lambda d^{+}(v)\rfloor$, $\lambda=0.6958\cdots$. This slightly improves the known results in $3$-free digraphs with large minimum out-degree. |
| Key words: Seymour's second neighborhood conjecture; 3-free digraph |