A generalization of a conjecture due to Erdős, Jacobson and Lehel

Abstract: An -graph is a loopless undirected graph in which no two vertices are joined by more than edges. An -complete graph on vertices, denoted by , is an -graph on vertices in which each pair of vertices is joined by exactly edges. A non-increasing sequence of nonnegative integers is -graphic if it is realizable by an -graph on vertices. Let be the smallest even integer such that each -term -graphic sequence with term sum of at least is realizable by an -graph containing as a subgraph. In this paper, we determine the value of for sufficiently large , which generalizes a conjecture due to Erdős, Jacobson and Lehel. [Copyright &y& Elsevier]