Geodesic
A proof of Erdős-Fishburn's conjecture for \(g(6)=13\)
Wei Xianglin1
1Hebei University of Science and Technology
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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A planar point set $X$ in the Euclidean plane is called a $k$-distance set if there are exactly $k$ distances between two distinct points in $X$. An interesting problem is to find the largest possible cardinality of a $k$-distance set. This problem was introduced by Erdős and Fishburn (1996). Maximum planar sets that determine $k$ distances for $k$ less than 5 have been identified. The 6-distance conjecture of Erdős and Fishburn states that 13 is the maximum number of points in the plane that determine exactly 6 different distances. In this paper, we prove the conjecture.
DOI : 10.37236/2917
Classification : 52C10
Mots-clés : 6-distance conjecture, diameter graph, independent set

Wei Xianglin  1

1 Hebei University of Science and Technology 
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     title = {A proof of {Erd\H{o}s-Fishburn's} conjecture for \(g(6)=13\)},
     journal = {The electronic journal of combinatorics},
     year = {2012},
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     number = {4},
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Wei Xianglin. A proof of Erdős-Fishburn's conjecture for \(g(6)=13\). The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2917

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