Covering the complete graph by partitions

@article{Fredi1989CoveringTC,
  title={Covering the complete graph by partitions},
  author={Zolt{\'a}n F{\"u}redi},
  journal={Discret. Math.},
  year={1989},
  volume={75},
  pages={217-226}
}
  • Z. Füredi
  • Published 1 September 1989
  • Computer Science, Mathematics
  • Discret. Math.
Monochromatic diameter-2 components in edge colorings of the complete graph
Gyarfas conjectured that in every r -edge-coloring of the complete graph K n there is a monochromatic component on at least n ∕ ( r − 1 ) vertices which has diameter at most 3. We show that for r = 3
Partitioning 3-Colored Complete Graphs into Three Monochromatic Cycles
TLDR
It follows that all the vertices of K^n can be partitioned into at most 17 monochromatic cycles, improving the best known bounds.
Vertex coverings by monochromatic cycles and trees
Large components in r-edge-colorings of Kn have diameter at most five
  • M. Ruszinkó
  • Mathematics, Computer Science
    J. Graph Theory
  • 2012
TLDR
It is shown in this note that every r-edge-coloring of Kn contains a monochromatic component of diameter at most five on at least n/(r−1) vertices.
Intersecting designs from linear programming and graphs of diameter two
  • Z. Füredi
  • Computer Science, Mathematics
    Discret. Math.
  • 1994
Bounding the pseudoachromatic index of the complete graph via projective planes
A Note About Monochromatic Components in Graphs of Large Minimum Degree
Abstract For all positive integers r ≥ 3 and n such that r2 − r divides n and an affine plane of order r exists, we construct an r-edge colored graph on n vertices with minimum degree (1−r-2r2-r{{r -
Weighted arcs, the finite radon transform and a Ramsey problem
We establish a link between the theory of (k, v)-arcs in affine planes and a graph theoretic Ramsey problem: A (n, k)-coloring of the complete graphKu is a coloring of the edges ofKu withk colours
Large Monochromatic Components in Edge Colorings of Graphs: A Survey
The aim of this survey is to summarize an area of combinatorics that lies on the border of several areas: Ramsey theory, resolvable block designs, factorizations, fractional matchings and coverings,
Intersecting designs from linear programming and graphs of diameter two *
We investigate l-designs (regular intersecting families) and graphs of diameter 2. The optimal configurations are either projective planes or design-like structures closely related to finite
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