A Note on Edge Colorings and Trees

A Note on Edge Colorings and Trees

We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal \(\kappa\) has a homogeneous set of size \(\kappa\) p...

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Veröffentlicht in:arXiv.org 2022-04
Hauptverfasser: Jarden, Adi, Shami, Ziv
Format: Artikel
Sprache:eng
Schlagworte:
Trees
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Zusammenfassung:We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal \(\kappa\) has a homogeneous set of size \(\kappa\) provided that the number of colors, \(\mu\) satisfies \(\mu^+
ISSN:2331-8422