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math.CO2026
Greedy Coloring and Simple Exponential Strengthenings of Brooks-Type Theorems
Alex Crane, Carl Feghali, Felicia Lucke +2
Brooks' Theorem is a foundational result in graph coloring: if a graph is connected, not a clique, and has maximum degree , then it admits a proper -coloring. In this p…
math.CO2026
Optimal b-Colourings and Fall Colourings in -Free Graphs
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke +3
In a colouring of a graph, a vertex is b-chromatic if it is adjacent to a vertex of every other colour. We consider four well-studied colouring problems: b-Chromatic Number, Tight…
math.CO2026
Steiner Forest for -Subgraph-Free Graphs
Tala Eagling-Vose, David C. Kutner, Felicia Lucke +4
Our main result is a full classification, for every connected graph , of the computational complexity of Steiner Forest on -subgraph-free graphs. To obtain this dichotomy, we…