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A note on potentially $K_4-e$ graphical sequences

Chunhui Lai
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Abstract

A sequence $S$ is potentially $K_4-e$ graphical if it has a realization containing a $K_4-e$ as a subgraph. Let $σ(K_4-e, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $σ(S)\geq σ(K_4-e, n)$ is potentially $K_4-e$ graphical. Gould, Jacobson, Lehel raised the problem of determining the value of $σ(K_4-e, n)$. In this paper, we prove that $σ(K_4-e, n)=2[(3n-1)/2]$ for $n\geq 7$, and $n=4,5,$ and $σ(K_4-e, 6)= 20$.

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Chunhui Lai. 2003-08-11. A note on potentially $K_4-e$ graphical sequences. https://arxiv.org/abs/math/0308105

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