On dense strongly Z2s+1-connected graphs

Let G be a graph and s>0 be an integer. If, for any function b:V(G)→Z2s+1 satisfying ∑v∈V(G)b(v)≡0(mod2s+1), G always has an orientation D such that the net outdegree at every vertex v is congruent to b(v) mod 2s+1, then G is strongly Z2s+1-connected. For a graph G, denote by α(G) the cardinality of a maximum independent set of G. In this paper, we prove that for any integers s,t>0 and real numbers a,b with 0