The seminars aim to promote the presence of discrete mathematics in Guangzhou, as well as to strengthen the discrete mathematics community there. Everyone is welcome to attend. If anyone is interested in giving a seminar talk, or for general enquiries, please contact one of the organisers.
Ping Hu: email@example.com
Henry Liu: firstname.lastname@example.org
Chao Yang: email@example.com
Zanbo Zhang: firstname.lastname@example.org
How to get to School of Mathematics, Sun Yat-sen University
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.