We introduce downward unary colorings, a particular case of additive colorings and show that it is a key notion in generalizing coloring theorems from the context of additive colorings to the context of locally-additive colorings. In addition, we give a full characterization of the downward unary colorings.

Ramsey, colorings, additive colorings.

Received: August 3, 2022; Revised: September 28, 2022; Accepted: October 18, 2022; Published: November 2, 2022

How to cite this article: Yonah Cherniavsky and Adi Jarden, Downward unary colorings, Advances and Applications in Discrete Mathematics 35 (2022), 1-10. http://dx.doi.org/10.17654/0974165822046

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Adi Jarden and Ziv Shami, A note on edge colorings and trees, Mathematical Logic Quarterly 167 (2022), 447-457.
[2] Saharon Shelah, The monadic theory of order, Annals of Mathematics 102(3) (1975), 379-419.