Seminar of Graph Theory - Yifan Zhang (5.3.2026)
Thursday 5.3.2026 at 9:50, Lecture room M 213
Yifan Zhang (University of Ostrava/VSB - Technical University of Ostrava):
Coverings of Complete Graphs by Small Cliques and Applications
Abstrakc:
We study coverings of complete graphs by small cliques, motivated by both design theory and by parallel fast Boundary Element Methods. When several clique sizes are allowed, minimising the number of blocks alone becomes less informative, so we instead optimise the “excess”, meaning the edges that get covered more than once, together with the block count. I will present sharp results for coverings using 3- and 4-cliques, discuss extensions that also allow 5-cliques (including remaining open cases), and explain how these constructions feed into practical load-balancing models for fast BEM.