Institution: | a Department of Applied Mathematics, College of Information Science and Technology, Hainan University, Haikou 570228, PR China b Department of Mathematics, Ningxia University, Yinchuan 750021, PR China c Department of Mathematics, Middlebury College, Middlebury, VT, USA |
Abstract: | Gould, Jacobson and Lehel R.J. Gould, M.S. Jacobson, J. Lehel, Potentially G-graphical degree sequences, in: Y. Alavi, et al. (Eds.), Combinatorics, Graph Theory and Algorithms, vol. I, New Issues Press, Kalamazoo, MI, 1999, pp. 451-460] considered a variation of the classical Turán-type extremal problems as follows: for any simple graph H, determine the smallest even integer σ(H,n) such that every n-term graphic sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2+?+dn≥σ(H,n) has a realization G containing H as a subgraph. Let Ft,r,k denote the generalized friendship graph on kt−kr+r vertices, that is, the graph of k copies of Kt meeting in a common r set, where Kt is the complete graph on t vertices and 0≤r≤t. In this paper, we determine σ(Ft,r,k,n) for k≥2, t≥3, 1≤r≤t−2 and n sufficiently large. |