Constructing nonorientable genus embedding of complete bipartite graph minus a matching

2023/05/17 by Lv, Shengxiang
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.10008

Abstract

G_m,n,k is a subgraph of the complete bipartite graph K_m,n with a k-matching removed. By a new method based on the embeddings of some G_m,n,k with small m,n,k and bipartite joins with small bipartite graphs, we construct the nonorientable genus embedding of G_m,n,k for all m,n≥ 3 with (m,n,k)≠ (5,4,4), (4,5,4),(5,5,5). Hence, we solve the cases G_n+1,n,n(n is even) and G_n,n,n, with the values of n that have not been previously solved, i.e., n≥ 6. This completes previous work on the nonorientable genus of G_m,n,k.

Related

• Settling the nonorientable genus of the nearly complete bipartite graphs
• Genus embeddings of complete graphs minus a matching
• Lower bound on the number of the maximum genus embedding of K_n,n
• Face distributions of embeddings of complete graphs
• Classification of nonorientable regular embeddings of complete bipartite graphs