## 28 Citations

Monochromatic diameter-2 components in edge colorings of the complete graph

- MathematicsInvolve, a Journal of Mathematics
- 2021

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

- MathematicsElectron. J. Comb.
- 2011

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

- Mathematics
- 2022

. 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…

Intersecting designs from linear programming and graphs of diameter two

- MathematicsDiscret. Math.
- 1994

Bounding the pseudoachromatic index of the complete graph via projective planes

- MathematicsElectron. Notes Discret. Math.
- 2008

A Note About Monochromatic Components in Graphs of Large Minimum Degree

- Mathematics
- 2020

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

- MathematicsGraphs Comb.
- 1991

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

- Mathematics
- 2011

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 *

- Mathematics
- 2001

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…

## References

SHOWING 1-5 OF 5 REFERENCES

On generalized ramsey numbers for trees

- MathematicsComb.
- 1985

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

- MathematicsComb.
- 1981

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

- MathematicsSIAM J. Discret. Math.
- 1988

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

- MathematicsComb.
- 1986

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.