TY - JOUR
TI - Noncrossing Monochromatic Subtrees and Staircases in 0-1 Matrices
VL - 2014
PY - 2014
DA - 2014/01/23
DO - 10.1155/2014/731519
UR - https://doi.org/10.1155/2014/731519
AB - The following question is asked by the senior author (Gyárfás (2011)). What is the order of the largest monochromatic noncrossing subtree (caterpillar) that exists in every 2-coloring of the edges of a simple geometric ? We solve one particular problem asked by Gyárfás (2011): separate the Ramsey number of noncrossing trees from the Ramsey number of noncrossing double stars. We also reformulate the question as a Ramsey-type problem for 0-1 matrices and pose the following conjecture. Every 0-1 matrix contains zeros or ones, forming a staircase: a sequence which goes right in rows and down in columns, possibly skipping elements, but not at turning points. We prove this conjecture in some special cases and put forward some related problems as well.
JF - Journal of Discrete Mathematics
SN - 2090-9837
PB - Hindawi Publishing Corporation
SP - 731519
KW -
A2 - Shiu, Wai Chee
AU - Cai, Siyuan
AU - Grindstaff, Gillian
AU - Gyárfás, András
AU - Shull, Warren
ER -