Potentially F2m+igraphic sequences

Abstract

Gould et al. considered a variation of the classical Turán-type extremal problems as follows: for a given graph H, determine the smallest even integer σ(H,n) such that every n-term graphic sequence π = (d _i,d₂,⋯,d_n) with σ(π) = d ₁ + d₂ +⋯ + d_n > σ(H,n) has a realization G containing H as a subgraph. In this paper, we determine the values of σ(F_2m+i,n) for m > 4, i ε {-1,0} and sufficiently large n, where F_2m+i is the fan graph on 2m + i vertices.