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A note on potentially $K_4-e$ graphical sequences | Chunhui Lai
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12 Aug 2003 | Journal: | Australasian Journal of Combinatorics, 24(2001), 123-127 | Subject: | Combinatorics MSC-class: 05C07; 05C35 | math.CO | Abstract: | 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 $ngeq 7$, and $n=4,5,$ and $sigma(K_4-e, 6)= 20$. | Source: | arXiv, math.CO/0308105 | Services: | Forum | Review | PDF | Favorites |
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