A new bound for the 2/3 conjecture

Details A new bound for the 2/3 conjecture A new bound for the 2/3 conjecture

2012-04-11

arxiv.org/abs/1204.2519v1

Computer Science

Discrete Mathematics

Scientific paper

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 et al. in 1989, is 22. It is conjectured that three
vertices suffice.

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