Connectivity And Odd-H-linked Graphs

An odd-H-subdivision in a graph G is a pair of mappings f: V(H)→V(G) and g:E(H) into the set of paths in G such that: (a) f(u)≠f(v) for all distinct u,v∈V(H);(b) for every uv∈E(H), g(uv) is an f(u),f(v)-path in G, and distinct edges map into internally disjoint paths in G; (c) g(uv) is an f(u) ,f(v) -path with odd length in G for every uv e E(H). A graph G is odd-H-linked if every injective mappingf:V(H)→V(G) can be extended to an odd-H-subdivision in G .In this paper, we will show that: If G is a 47k -connected graph and bi(G)≥3k-2 ,then G is odd-C_k-linked.