2024/11/29 by Yihan Chen, Jialin He, Chen, Yihan +9
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2411.19773
openalex publication_date 2024/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1975 Bollobás, Erdős, and Szemerédi asked what minimum degree guarantees an octahedral subgraph K3(2) in any tripartite graph G with n vertices in each vertex class. We show that δ(G)≥ n+2n(5)/(6) suffices thus improving the bound n+(1+o(1))n(11)/(12) of Bhalkikar and Zhao obtained by following their approach. Bollobás, Erdős, and Szemerédi conjectured that n+cn(1)/(2) suffices and there are many K3(2)-free tripartite graphs G with δ(G)≥ n+cn(1)/(2). We confirm this conjecture under the additional assumption that every vertex in G is adjacent to at least (1/5+ε)n vertices in any other vertex class.