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math.CO2026
An 18-colour bound for locally irregular decompositions
Carla Negri Lintzmayer, Guilherme Oliveira Mota, Maycon Sambinelli +1
A graph is locally irregular if adjacent vertices have distinct degrees. A graph G is decomposable if its edge set can be decomposed into locally irregular graphs, and its locally…
math.CO2026
Proper conflict-free 7-coloring of planar graphs
A. Jiménez, C. N. Lintzmayer, M. Sambinelli
A proper conflict-free coloring is a proper vertex coloring in which every nonisolated vertex has a color occurring uniquely in its open neighborhood. We prove that every graph wit…