A Havel-Hakimi type procedure and a sufficient condition for a sequence to be potentially S
r,s
-graphic |
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Authors: | Jian-Hua Yin |
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Institution: | 1. Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, P.R. China
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Abstract: | The split graph K r + $\overline {{K_s}} $ on r+s vertices is denoted by S r,s . A non-increasing sequence π = (d 1, d 2, …, d n ) of nonnegative integers is said to be potentially S r,s -graphic if there exists a realization of π containing S r,s as a subgraph. In this paper, we obtain a Havel-Hakimi type procedure and a simple sufficient condition for π to be potentially S r,s -graphic. They are extensions of two theorems due to A.R.Rao (The clique number of a graph with given degree sequence, Graph Theory, Proc. Symp., Calcutta 1976, ISI Lect. Notes Series 4 (1979), 251–267 and An Erd?s-Gallai type result on the clique number of a realization of a degree sequence, unpublished). |
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