On potentially H-graphic sequences
Meng-Xiao Yin, Jian-Hua Yin · Czechoslovak Mathematical Journal · 2007
For given a graph H, a graphic sequence π = (d 1, d 2,..., d n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K 5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K 5-graphic, where K r is a complete graph on r vertices and K r-e is a graph obtained from K r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence π to be potentially K 6-graphic.