Rose McCarty

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math.CO2025

Decomposing a signed graph into rooted circuits

Rose McCarty

We prove a precise min-max theorem for the following problem. Let $G$ be an Eulerian graph with a specified set of edges $S \subseteq E (G)$ , and let $b$ be a vertex of $G$ . Then wh…

math.CO2024

Prime and polynomial distances in colourings of the plane

James Davies, Rose McCarty, MichaÅ Pilipczuk

We give two extensions of the recent theorem of the first author that the odd distance graph has unbounded chromatic number. The first is that for any non-constant polynomial $f$ w…