Discrete Mathematics & Theoretical Computer Science, Vol 7 (2005)

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DMTCS vol 7 no 1 (2005), pp. 75-80

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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