The graph Ramsey number R(G,H) is the smallest integer r such that every 2-coloring of the edges of Kr contains either a red copy of G or a blue copy of H. The star-critical Ramsey number r∗(G,H) is the smallest integer k such that every 2-coloring of the edges of Kr − K1,r−1−k contains either a red copy of G or a blue copy of H. We will classify the critical graphs, 2-colorings of the complete graph on R(G,H) − 1 vertices with no red G or blue H, for the path-path Ramsey number. This classification will be used in the proof of r∗(Pn, Pm).
@article{bwmeta1.element.doi-10_7151_dmgt_1827,
author = {Jonelle Hook},
title = {
Critical Graphs for R(P
n
, P
m
) and the Star-Critical Ramsey Number for Paths
},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {689-701},
zbl = {1327.05228},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1827}
}
Jonelle Hook.
Critical Graphs for R(P
n
, P
m
) and the Star-Critical Ramsey Number for Paths
. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 689-701. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1827/
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