Covering multigraphs with bipartite graphs

04/23/2023

∙

by   Jaehoon Kim, et al.

∙

0

∙

share

Hansel's lemma states that ∑_H∈ℋ|H| ≥ n log_2 n holds where ℋ is a collection of bipartite graphs covering all the edges of K_n. We generalize this lemma to the corresponding multigraph covering problem and the graphon covering problem. We also prove an upper bound on ∑_H∈ℋ|H| which shows that our generalization is asymptotically tight in some sense.