Size of monochromatic components in local edge colorings

Edge colorings of complete graphs without tricolored triangles

We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings. We also determine the size of largest monochromatic stars guaranteed to occur. 2004 Wiley Periodicals, Inc. J Graph Theory 46: 211–216, 2004

Size of Monochromatic Double Stars in Edge Colorings

It is known that for r ≥ 2, there is a monochromatic component of size at least n r−1 in every r-coloring of the edges of Kn, the complete graph on n vertices (the result is sharp for infinitely many r and n). Here we show that one can say also something about the shape of the large component: for r ≥ 3 there is a monochromatic double star of size at least n r−1 in every r-coloring of the edges...

Vertex-Coloring with Defects

Defective coloring is a variant of the traditional vertex-coloring in which adjacent vertices are allowed to have the same color, as long as the induced monochromatic components have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, diameter, and acyc...

Un co rre cte d Pr oo f Large Monochromatic Components in Edge 1 Colorings of Graphs : A Survey

Partition of Graphs and Hypergraphs into Monochromatic Connected Parts

We show that two results on covering of edge colored graphs by monochromatic connected parts can be extended to partitioning. We prove that for any 2-edgecolored non-trivial r-uniform hypergraph H, the vertex set can be partitioned into at most α(H)− r+ 2 monochromatic connected parts, where α(H) is the maximum size of a set of vertices that does not contain any edge. In particular, any 2-edgec...