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A note on potentially $K_4-e$ graphical sequences

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:2402.06002

Australas. J. Combin. , 24, 123–127, 2001.9
"A sequence $S$ is potentially $K_4-e$ graphical if it has a realization containing a $K_4-e$ as a subgraph. Let $\sigma(K_4-e,n)$ denote the smallest degree sum such that every $n$ -term graphical sequence $S$ with $\sigma(S)\geq\sigma(K_4-e,n)$ is potentially $K_4-e$ graphical. Gould, Jacobson, Lehel raised the problem of determining the value of $\sigma(K_4-e,n)$ . In this paper, we prove that $\sigma(K_4-e,n)=2[(3n-1)/2]$ for $n\geq7$ and $n=4,5$ , and $\sigma(K_4-e,6)=20$ .''
graphical sequences: $K_4-e$
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@inproceedings{lai2001a,
  title={A note on potentially $K_4-e$ graphical sequences},
  author={Lai Chunhui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20240210111919548689765},
  booktitle={Australas. J. Combin. },
  volume={24},
  pages={123–127},
  year={2001},
}
Lai Chunhui. A note on potentially $K_4-e$ graphical sequences. 2001. Vol. 24. In Australas. J. Combin. . pp.123–127. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20240210111919548689765.
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