We establish new lower bounds for $28$ classical two and three color Ramsey numbers, and describe the heuristic search procedures used. Several of the new three color bounds are derived from the two color constructions; specifically, we were able to use $(5,k)$-colorings to obtain new $(3,3,k)$-colorings, and $(7,k)$-colorings to obtain new $(3,4,k)$-colorings. Some of the other new constructions in the paper are derived from two well known colorings: the Paley coloring of $K_{101}$ and the cubic coloring of $K_{127}$.
@article{10_37236_5254,
author = {Geoffrey Exoo and Milos Tatarevic},
title = {New lower bounds for 28 classical {Ramsey} numbers},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/5254},
zbl = {1327.05227},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5254/}
}
TY - JOUR
AU - Geoffrey Exoo
AU - Milos Tatarevic
TI - New lower bounds for 28 classical Ramsey numbers
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/5254/
DO - 10.37236/5254
ID - 10_37236_5254
ER -
%0 Journal Article
%A Geoffrey Exoo
%A Milos Tatarevic
%T New lower bounds for 28 classical Ramsey numbers
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/5254/
%R 10.37236/5254
%F 10_37236_5254
Geoffrey Exoo; Milos Tatarevic. New lower bounds for 28 classical Ramsey numbers. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5254
