Geodesic
Note on Gy. Elekes's conjectures concerning unavoidable patterns in proper colorings
The electronic journal of combinatorics, Tome 7 (2000)
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A counterexample is presented to Gy. Elekes's conjecture concerning the existence of long $2$-colored paths in properly colored graphs. A modified version of the conjecture is given and its connections to a problem of Erdős - Gyárfás and to Szemerédi's theorem are examined.
DOI : 10.37236/1541
Classification : 05C15, 05C55, 05C38
Mots-clés : Elekes's conjecture, colored graphs 
@article{10_37236_1541,
     author = {Vera Rosta},
     title = {Note on {Gy.} {Elekes's} conjectures concerning unavoidable patterns in proper colorings},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1541},
     zbl = {0939.05034},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1541/}
}
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%J The electronic journal of combinatorics
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Vera Rosta. Note on Gy. Elekes's conjectures concerning unavoidable patterns in proper colorings. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1541

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