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Abstract The systematic study of Turán-type extremal problems for edge-ordered graphs was initiated by Gerbner et al. (Turán problems for Edge-ordered graphs, 2021). They conjectured that the extremal functions of edge-ordered forests of order chromatic number 2 are n^1+o (1) n 1 + o (1). Here we resolve this conjecture proving the stronger upper bound of n2^O (n) n 2 O (log n). This represents a gap in the family of possible extremal functions as other forbidden edge-ordered graphs have extremal functions (nᶜ) Ω (n c) for some c>1 c > 1. However, our result is probably not the last word: here we conjecture that the even stronger upper bound of n ^O (1) n n log O (1) n also holds for the same set of extremal functions.
Kucheriya et al. (Fri,) studied this question.