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Graphs and Combinatorics

, Volume 8, Issue 4, pp 323–332 | Cite as

Monochromatic Vs multicolored paths

  • Hanno Lefmann
  • Vojtěch Rödl
  • Robin Thomas
Original Papers

Abstract

Letl andk be positive integers, and letX={0,1,...,lk−1}. Is it true that for every coloring δ:X×X→{0,1,...} there either exist elementsx0<x1<...<xl ofX with δ(x0,x1)=δ(x1,x2)=...=δ(xl−1,xl), or else there exist elementsy0<y1<...<yk ofX with δ(yi−1,yi) ∈ δ(yj−1,yj) for all 1<-i<jk? We prove here that this is the case if eitherl≤2, ork≤4, orl≥(3k)2k. The general question remains open.

Keywords

Positive Integer General Question 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Hanno Lefmann
    • 1
    • 2
  • Vojtěch Rödl
    • 3
  • Robin Thomas
    • 4
  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  4. 4.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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