An extremal problem on the potentially wheel graph sequences

Abstract

Gould, Jacobson and Lehel considered a variation of the classical Turán-type extremal problems: for a given graph H₁ determine the smallest even integer σ(H, n) such that every n-term graphic sequence π = (d₁,d₂,⋯, d_n) with σ(π) = d₁ + d₂ + ⋯ + d_n ≥ σ(H, n) has a realization G containing H as a, subgraph. In this paper, we determine the values of σ(W_r,n) for r ≥ 6 and n sufficiently large, where W_r is the wheel graph on r vertices.