Large Topological Cliques in Graphs Without a 4-Cycle

Mader asked whether every C4-free graph G contains a subdivision of a complete graph whose order is at least linear in the average degree of G. We show that there is a subdivision of a complete graph whose order is almost linear. More generally, we prove that every Ks,t-free graph of average degree r contains a subdivision of a complete graph of order r 1 2 + 1 2(s-1) -o(1) .

• Type: Journal
• Year: 2004
• Where: CPC
• Authors: Daniela Kühn, Deryk Osthus
• Keywords: Average Degree, C4-free Graph, Complete Graph, CPC 2004