Two sufficient conditions for a graphic sequence to have a realization with prescribed clique size

A graphic sequence π = ( d 1 , d 2 , … , d n ) is said to be potentially K r + 1 -graphic, if π has a realization G containing K r + 1 , a clique of r + 1 vertices, as a subgraph. In this paper, we give two simple sufficient conditions for a graphic sequence π = ( d 1 , d 2 , … , d n ) to be potenti...

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