Discrete Mathematics & Theoretical Computer Science
Volume 7 n° 1 (2005), pp. 75-80
| author: | Chunhui Lai |
|---|---|
| title: | An extremal problem on potentially Kp,1,1-graphic sequences |
| keywords: | graph; degree sequence; potentially Kp,1,1-graphic |
| abstract: | A sequence S is potentially Kp,1,1 graphical if it has a realization containing a Kp,1,1 as a subgraph, where Kp,1,1 is a complete 3-partite graph with partition sizes
p,1,1. Let σ(Kp,1,1, n) denote the smallest degree sum
such that every n-term graphical sequence S with σ(S)≥
σ(Kp,1,1, n) is potentially Kp,1,1 graphical. In this
paper, we prove that σ (Kp,1,1, n)≥ 2[((p+1)(n-1)+2)/2]
for n ≥ p+2. We conjecture that equality holds for n ≥
2p+4. We prove that this conjecture is true for p = 3.
AMS Subject Classifications: 05C07, 05C35
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| reference: | Chunhui Lai (2005), An extremal problem on potentially Kp,1,1-graphic sequences, Discrete Mathematics and Theoretical Computer Science 7, pp. 75-80 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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