# Discrete Mathematics & Theoretical Computer Science

## Volume 7 n° 1 (2005), pp. 75-80

author: | Chunhui Lai |
---|---|

title: | An extremal problem on potentially K_{p,1,1}-graphic sequences |

keywords: | graph; degree sequence; potentially K_{p,1,1}-graphic |

abstract: | A sequence S is potentially K graphical if it has a realization containing a _{p,1,1}K as a subgraph, where _{p,1,1}K is a complete 3-partite graph with partition sizes
_{p,1,1}p,1,1. Let σ(K denote the smallest degree sum
such that every _{p,1,1}, n)n-term graphical sequence S with σ(S)≥
σ(K is potentially _{p,1,1}, n)K graphical. In this
paper, we prove that _{p,1,1}σ (K
for _{p,1,1}, n)≥ 2[((p+1)(n-1)+2)/2]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 K_{p,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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Automatically produced on Sun May 22 22:02:34 CEST 2005 by falk