Discrete Mathematics & Theoretical Computer Science
| 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
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |
| 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. |
| ps.gz-source: | dm070107.ps.gz (63 K) |
| ps-source: | dm070107.ps (161 K) |
| pdf-source: | dm070107.pdf (93 K) |
The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.
Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.