Author

V. D. dos Santos

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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

A rainbow version of Lehel's conjecture

Lehel's conjecture states that every 2-edge-colouring of K_n admits a partition of its vertex set into two monochromatic cycles. It was proven for sufficiently large n by {\L}uczak, R\"odl, and Szemer\'edi in 1998, later improved by Allen in 2008, and fully resolved by Bessy and Thomass\'e in 2010. In this paper, we co...

Pedro Araújo, Xiao-Chuan Liu, Taísa L. Martins et al. · 0 citations