TY - JOUR
T1 - New values for the bipartite Ramsey number of the four-cycle versus stars
AU - Mattheus, Sam
AU - Héger, Tamás
AU - Hatala, Imre
PY - 2021/5
Y1 - 2021/5
N2 - We provide new values of the bipartite Ramsey number RB(C4,K1,n) using induced subgraphs of the incidence graph of a projective plane. The approach, based on deleting subplanes of projective planes, has been used in related extremal problems and allows us to unify previous results and extend them. More importantly, using deep stability results on 2modp sets and double blocking sets, we can show some of the limits of this technique when the projective plane is Desarguesian of large enough square order. Finally, we also disprove two conjectures about RB(C4,K1,n).
AB - We provide new values of the bipartite Ramsey number RB(C4,K1,n) using induced subgraphs of the incidence graph of a projective plane. The approach, based on deleting subplanes of projective planes, has been used in related extremal problems and allows us to unify previous results and extend them. More importantly, using deep stability results on 2modp sets and double blocking sets, we can show some of the limits of this technique when the projective plane is Desarguesian of large enough square order. Finally, we also disprove two conjectures about RB(C4,K1,n).
UR - http://www.scopus.com/inward/record.url?scp=85101346788&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2021.112320
DO - 10.1016/j.disc.2021.112320
M3 - Article
VL - 344
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 5
M1 - 112320
ER -