Ordered matchings with interval chromatic number 2

Close the gap between the upper and lower bounds for ordered Ramsey numbers of ordered matchings with interval chromatic number 2.

Background

For ordered matchings whose vertices can be partitioned into two independent intervals, the survey gives an O(n2) upper bound and an almost-sure lower bound of order (n/log n)2. The cited problem asks to determine the correct asymptotic scale.

References

Similarly, as in the case of general ordered matchings, there is a gap between the lower and upper bound. Thus, Colon, Fox, Lee, and Sudakov posed the following problem for ordered matchings with interval chromatic number 2.

Close the gap between the upper and lower bounds for ordered Ramsey numbers of ordered matchings with interval chromatic number 2.

— A Survey on Ordered Ramsey Numbers  (2502.02155 - Balko, 4 Feb 2025) in Problem following Theorem (thm-oderRam-bipMatching), Section 2

Close the gap between the upper and lower bounds for ordered Ramsey numbers of ordered matchings with interval chromatic number 2.

— A Survey on Ordered Ramsey Numbers  (2502.02155 - Balko, 4 Feb 2025) in Problem following Theorem (thm-oderRam-bipMatching), Section 2, subsection “Bounded degrees and interval chromatic number”