On the potential function of an arbitrary graph<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si25.svg"><mml:mi>H</mml:mi></mml:math>

Given a graph H, a graphic sequence π is potentially H-graphic if there is a realization of π containing H as a subgraph. In 1991, Erdős, Jacobson and Lehel introduced the following problem: determine the minimum even integer σ(H,n) such that each n-term graphic sequence with sum at least σ(H,n) is potentially H-graphic. This problem can be viewed as a “potential” degree sequence relaxation of the Turán problems. For an arbitrary graph H of...