The Characterization for a Graphic Sequence to have a Realization Containing K1,1,s
The Characterization for a Graphic Sequence to have a Realization Containing K1,1,s
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DOI：
10.1007/s00373-011-1061-y
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发表时间：
2012-07
影响因子：
0.7
通讯作者：
Jianhua Yin
中科院分区：
文献类型：
--
作者：
Jianhua Yin
A graphic sequenceπ= (d1,d2, . . . ,dn) is said to be potentiallyK1,1,s-graphic if there is a realization ofπcontainingK1,1,sas a subgraph, whereK1,1,sis the 1 × 1 ×scomplete 3-partite graph. In this paper, a simple characterization of potentiallyK1,1,s-graphic sequences fors≥ 2 andn≥ 3s+ 1 is obtained. This characterization implies Lai’s conjecture onσ(K1,1,s,n), which was confirmed by J.H. Yin, J.S. Li and W.Y. Li, and the values ofσ(K2,s,n) fors≥ 4 andn≥ 3s+ 1, whereK2,sis the 2 ×scomplete bipartite graph.
