Speaker: Hong Wang, professor, University of Idaho

Date: June 21, 2024

Time: 15:00-16:00

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Let D = (V,A) be a directed graph of order n with n≥ 9. Suppose that every vertex of D has degree at least 3n/2. Then for any two independent arcs fand g in D and any integer partition n = n₁+ n₂ with n₁≥4 and n₂≥4, D contains two disjoint directed cycles C₁ and C₂ of orders n₁and n₂, respectively such that C₁ contains fand C₂contains g. Moreover, the condition is sharp. We conjecture that if every vertex of D has degree at least (3n + 2k-4)/2 then for any k independent arcs f₁,..., f_k of D and any integer partition n = n₁+...+ n_k with n_i≥4 for all1≤i≤k, D has k disjoint directed cycles C₁,...,C_k of orders n₁,...,n_k, respectively such that f₁is an arc of C_i for all 1≤i≤k.

For more information, please visit:

https://view.sdu.edu.cn/info/1020/192486.htm