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A new class of Ramsey–Turán problems

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
310
Issue
24
Identifiers
DOI: 10.1016/j.disc.2010.09.009
Keywords
  • Ramsey–Turán Problems
  • Minimum Degree
  • Monochromatic Cycles

Abstract

Abstract We introduce and study a new class of Ramsey–Turán problems, a typical example of which is the following one: Let ε > 0 and G be a graph of sufficiently large order n with minimum degree δ ( G ) > 3 n / 4 . If the edges of G are colored in blue or red, then for all k ∈ [ 4 , ⌊ ( 1 / 8 − ε ) n ⌋ ] , there exists a monochromatic cycle of length k .

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