Author

M. Sambinelli

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Preprint Sep 2026

An 18-colour bound for locally irregular decompositions

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 irregular chromatic index lir(G) is the least number of graphs in such a decomposition. We prove that lir(G)<= 18 for every decomposable gra...

C. Lintzmayer, G. Mota, M. Sambinelli et al. · 0 citations

Preprint Aug 2026

Proper conflict-free 7-coloring of planar graphs

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 with neither a $K_5$-minor nor a $Q_6$-minor admits such a coloring with at most seven colors, where $Q_6=K_3\vee\overline{K_3}$. In particular...

A. Jiménez, C. Lintzmayer, M. Sambinelli · 1 citation