A note on potentially \(K_4-e\) graphical sequences (Q2760432)

Let \(H\) be a graph. A graphical sequence \(S\) is potentially \(H\)-graphical if there is a realization of \(S\) containing \(H\) as a subgraph. The author studies the problem of determining the minimum even integer \(m\) such that every \(n\)-term graphical sequence \(S\) with \(\sigma(S)\geq m\) is potentially \(H\)-graphical. This number \(m\) is denoted by \(\sigma(H,n)\). The author continues the study of \(\sigma(H,n)\) and determines the exact value of \(\sigma(K_4-e,n)\) for \(n\geq 4\).