Potentially F2m+i-graphic sequences

Gould et al. considered a variation of the classical Turan-type extremal problems as follows: for a given graph H, determine the smallest even integer sigma(H, n) such that every n-term graphic sequence pi = (d(1), d(2), ... , d(n)) with sigma(pi) = d(1) + d(2) + ... + d(n) >= sigma(H, n) has a realization G containing H as a subgraph. In this paper, we determine the values of sigma(F2m+i, n) for m >= 4, i is an element of {-1, 0} and sufficiently large n, where F2m+i is the fan graph on 2m + i vertices.