Bounded skewness–excess gap for complete and complete bipartite graphs

Prove that the maximum difference between the t-skewness μ_t and the integer Euler lower bound ε_t, taken over all complete graphs and complete bipartite graphs and all orientable surfaces S_t, is finite.

Background

The paper establishes that μ_t = ε_t for all orientable surfaces for hypercubes and folded cubes, while surveying results for complete and complete bipartite graphs. It then proposes a broader conjecture that the discrepancy between skewness and the integer Euler lower bound remains uniformly bounded across those two graph families and all orientable surfaces.

Here ε_t(G) = max{0, ⌈δ_t(G)⌉}, and the general inequalities are ε_t(G) ≤ μ_t(G) ≤ ν_t(G). The conjecture asks for a global finiteness result rather than equality in every case.