TY - JOUR
T1 - Offline thresholds for Ramsey-type games on random graphs
AU - Krivelevich, Michael
AU - Spöhel, Reto
AU - Steger, Angelika
PY - 2010/1
Y1 - 2010/1
N2 - In this article, we compare the offline versions of three Ramsey-type one-player games that have been studied in an online setting in previous work: the online Ramsey game, the balanced online Ramsey game, and the Achlioptas game. The goal in all games is to color the edges of the random graph Gn,m according to certain rules without creating a monochromatic copy of some fixed forbidden graph H. Although in general, the three online games have different thresholds, we prove that for most graphs H, the offline threshold for all three problems is m0(n) = n2-1/m2(H), where m2(H):= maxH'⊆H(eH' - 1)/(vH' - 2).
AB - In this article, we compare the offline versions of three Ramsey-type one-player games that have been studied in an online setting in previous work: the online Ramsey game, the balanced online Ramsey game, and the Achlioptas game. The goal in all games is to color the edges of the random graph Gn,m according to certain rules without creating a monochromatic copy of some fixed forbidden graph H. Although in general, the three online games have different thresholds, we prove that for most graphs H, the offline threshold for all three problems is m0(n) = n2-1/m2(H), where m2(H):= maxH'⊆H(eH' - 1)/(vH' - 2).
KW - Achlioptas process
KW - Ramsey properties
KW - Random graph
UR - http://www.scopus.com/inward/record.url?scp=70749083899&partnerID=8YFLogxK
U2 - 10.1002/rsa.20294
DO - 10.1002/rsa.20294
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:70749083899
SN - 1042-9832
VL - 36
SP - 57
EP - 79
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
IS - 1
ER -