Cycles in Random Bipartite Graphs

الأصل · EN

In this paper we study cycles in random bipartite graph G(n,n,p). We prove that if p≫ n⁻²/³, then G(n,n,p) a.a.s. satisfies the following. Every subgraph G'⊂ G(n,n,p) with more than (1+o(1))n²p/2 edges contains a cycle of length t for all even t∈[4,(1+o(1))n/30]. Our theorem complements a previous result on bipancyclicity, and is closely related to a recent work of Lee and Samotij.