The Interactive Sum Choice Number of Trees

TL;DR

This paper investigates the interactive sum choice number in trees, providing a recursive formula for forests, establishing its equivalence with the slow coloring cost, and answering an open question in the field.

Contribution

It introduces a recursive formula for the interactive sum choice number of forests and proves its equality with the slow coloring cost, resolving an open problem.

Findings

Recursive formula for forests' interactive sum choice number

Equality of interactive sum choice number and slow coloring cost on forests

Answers a question posed by Bonamy and Meeks

Abstract

We study the interactive sum choice number, a game coloring parameter introduced by Bonamy and Meeks, and obtain a recursive formula for the interactive sum choice number of forests. This formula coincides with a formula for the slow coloring cost of forests, a parameter introduced by Mahoney, Puleo, and West, and shows that these parameters are equal on forests. This answers a question of Bonamy and Meeks.