Author

G. Mota

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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

Monochromatic components in dense 2-edge-coloured balanced bipartite graphs

We prove that each $2$-edge-coloured spanning subgraph $G$ of $K_{n,n}$ with $\delta(G)\ge \lfloor (2n+1)/3 \rfloor$ can be covered by at most three monochromatic components. We provide a $2$-edge-coloured spanning subgraph of $K_{n,n}$ showing this minimum degree condition is sharp.

César Bispo, George Kontogeorgiou, M. Lage et al. · 0 citations