Talbot, JM;
Sanitt, A;
(2015)
An exact Turan result for tripartite 3-graphs.
The Electronic Journal of Combinatorics
, 22
(4)
, Article 4.3.
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Abstract
Mantel’s theorem says that among all triangle-free graphs of a given order the balanced complete bipartite graph is the unique graph of maximum size. We prove an analogue of this result for 3-graphs. Let K− 4 = {123, 124, 134}, F6 = {123, 124, 345, 156} and F = {K− 4 , F6}: for n 6= 5 the unique F-free 3-graph of order n and maximum size is the balanced complete tripartite 3-graph S3(n) (for n = 5 it is C (3) 5 = {123, 234, 345, 145, 125}). This extends an old result of Bollob´as that S3(n) is the unique 3-graph of maximum size with no copy of K− 4 = {123, 124, 134} or F5 = {123, 124, 345}.
| Type: | Article |
|---|---|
| Title: | An exact Turan result for tripartite 3-graphs |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://www.combinatorics.org/ojs/index.php/eljc/ar... |
| Language: | English |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1529897 |
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