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The Quest for Triangle-Free Colorings of the Complete Graph

Stanislaw P. Radziszowski

Department of Computer Science

Rochester Institute of Technology

spr@cs.rit.edu
### ABSTRACT

We study the question of whether one can color all the edges of
the complete graph K_n with k colors so that monochromatic
triangles are avoided. The largest n for which such coloring
exists defines the classical multicolor Ramsey number
R_k(3). This talk will overview the state of our knowledge of
this problem for three and more colors.

An algorithmic approach was successfully used to improve the upper
bound and to understand better the best known lower bound 51<=R_4(3).
In particular, in a joint work with Susan Fettes, we reproduce
the results obtained by Richard Kramer in his amazing
unpublished manuscript claiming that R_4(3)<=62.

Colloquia Series page.