Talbot, JM;
Baber, R;
(2014)
A solution to the 2/3 conjecture.
SIAM Journal on Discrete Mathematics
, 28
(2)
pp. 756-766.
10.1137/130926614.
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Abstract
We prove a vertex domination conjecture of Erd˝os, Faudree, Gould, Gy´arf´as, Rousseau, and Schelp that for every n-vertex complete graph with edges colored using three colors there exists a set of at most three vertices which have at least 2n/3 neighbors in one of the colors. Our proof makes extensive use of the ideas presented in [D. Kr´al’ et al., A new bound for the 2/3 conjecture, Combin. Probab. Comput. 22 (2013), pp. 384–393].
| Type: | Article |
|---|---|
| Title: | A solution to the 2/3 conjecture |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/130926614 |
| Publisher version: | http://doi.org/10.1137/130926614 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Vertex domination, Ramsey theory |
| 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/1529895 |
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