A new bound for the 2/3 conjecture

Abstract : We show that any n-vertex complete graph with edges colored with three colors contains a set of at most four vertices such that the number of the neighbors of these vertices in one of the colors is at least 2n/3. The previous best value, proved by Erdos, Faudree, Gould, Gyárfás, Rousseau and Schelp in 1989, is 22. It is conjectured that three vertices suffice.


https://hal.archives-ouvertes.fr/hal-00686989
Contributor : Jean-Sébastien Sereni <>
Submitted on : Thursday, January 3, 2013 - 11:03:58 AM
Last modification on : Tuesday, January 8, 2013 - 3:49:50 PM

Files

kls+12.pdf
fileSource_public_author

Identifiers

  • HAL Id : hal-00686989, version 2
  • ARXIV : 1204.2519

Collections

Citation

Daniel Král', Chun-Hung Liu, Jean-Sébastien Sereni, Peter Whalen, Zelealem Yilma. A new bound for the 2/3 conjecture. 2012. <hal-00686989v2>

Export

Share

Metrics

Consultation de
la notice

134

Téléchargement du document

40