Covering the complete graph by partitions

  title={Covering the complete graph by partitions},
  author={Zolt{\'a}n F{\"u}redi},
  journal={Discret. Math.},
  • Z. Füredi
  • Published 1 September 1989
  • 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
It follows that all the vertices of K^n can be partitioned into at most 17 monochromatic cycles, improving the best known bounds.
Monochromatic components with many edges
. Given an r -edge-coloring of the complete graph K n , what is the largest number of edges in a monochromatic connected component? This natural question has only recently received the attention it
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


On generalized ramsey numbers for trees
These numbers can be viewed as a generalization of the concept of Ramsey numbers, the class J, of all trees with n edges replacing an individual such tree.
Maximum degree and fractional matchings in uniform hypergraphs
This paper proves a corollary to a more general theorem on not necessarily intersecting hypergraphs, and says that ℋ is intersecting if for anyH,H′ ∈ℋ H ∩H′ ≠ 0.
On the Fractional Covering Number of Hypergraphs
It is shown (among other things) that for any rational $p/q\geqq 1$, there is a 3-uniform hypergraph H with $\tau* ( H ) = p/q$.
Finite projective spaces and intersecting hypergraphs
The results in this paper show that whereq is a prime power andn is sufficiently large, (n >n (k, c)) then the corresponding lower bound is given by the following construction.