Guangzhou Discrete Mathematics Seminar

Talks in 2020

2020.1

7 January 2020 (Tuesday), 3-4pm, *room 519*

Jiaao Li (Nankai University, Tianjin, China) From map coloring to nowhere-zero flows Poster

Planar graphs are vertex 4-colorable, and even 3-colorable if triangle-free. These results are known as 4CT and Grötzsch’s 3CT. Is there a better coloring for planar graphs with larger girth? A conjecture of Jaeger states that planar graphs of girth 2k are circular (2 + 2/k)-colorable, where the cases k = 1, 2 correspond to 4CT and 3CT. We provide partial results for the open cases k = 4, 6 and for the more general dual setting of nowhere-zero flows. Dually, Tutte’s and Jaeger’s flow conjectures predict existence of flows for highly connected graphs, and Lovász, Thomassen, Wu and Zhang (2013) showed that every 6p-edge-connected graph admits a circular (2 + 1/p)-flow. In this talk, we obtain circular (2 + 2/(2p − 1))-flow and (< 2 + 1/p)-flow for (6p − 2)- and (6p + 2)-edge-connected graphs, respectively.

2020 will be remembered as a very difficult year for all of us, because of the Covid-19 pandemic. We were only able to organise one seminar talk for the whole year as a result.