报告学者：Rong Luo

报告者单位：西弗尼吉亚大学

报告时间：2024年7月4日（周四）21:00--22:00

报告地点：线上腾讯会议：827-280-4645

报告摘要： The  modulo flow is a powerful tool in the study of flows of both ordinary graphs and signed graphs. For ordinary graphs, Tutte showed that a graph admits a nowhere-zero $k$-flow if and only if it admits a nowhere-zero $\Z_k$-flow. However, such equivalence does not hold any more for signed graphs.  Ma\v{c}ajova  and \v{S}koviera [\SIAMDM~31 (2017) 1937-1952] proved that every flow-admissible signed graph admitting a  nowhere-zero $\Z_2$-flow admits a nowhere-zero $4$-flow.  DeVos at al. [\JCTB~149 (2021) 198-221] proved that every signed graph admitting a nowhere-zero $\Z_3$-flow admits a nowhere-zero $5$-flow. DeVos also show that for each prime $k\geq 3$, every signed graph admitting a nowhere-zero $\Z_k$-flow admits a nowhere-zero $2k$-flow. In this paper, we prove the following two results:

(1) Every flow-admissible signed graph with a nowhere-zero $\Z_4$-flow admits a  nowhere-zero $8$-flow.

(2)  Every bridgeless signed graph with a nowhere-zero $\Z_5$-flow admits a nowhere-zero $7$-flow.

Combining the known results, we have  that  for each integer $k\geq 2$, every flow-admissible signed graph admitting a nowhere-zero $\Z_k$-flow admits a nowhere-zero $2k$-flow. 

Joint work with Miaomiao Han, Jiaao Li, You Lu.