On the potential number of Kr+i — E(H) *
Abstract
A graphic sequence it = (d1, d2, • • •,d3) is potentially Km — E(H)graphic if there exists a realization of π containing Km — E(H) as a subgraph, where H is & subgraph of Km and Km — E(H) refers to the graph obtained from Km by removing the edge set E(H). Let o(Km — E(H), n) be the smallest even integer such mat every n-term graphic sequence π with σ(π) > o(Km - E(H),n) is potentially Km - E(H)-pvpìàc, where H = di+daH \-dn- In this paper, we determine the value - E(H),n)forn > 3 r + 7, r + 1 > k ≥ 7 and j ≥ 6, where H is a graph on*: vertices and j edges which contains a graph Ks U Ai.s but contains none of Ct, Z4 or Ps (P* is a path of length k and Z4 is referred toas A'* — E(P¡)), which solves an open problem due to Lai and Hu 7. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.
