An undirected simple graphG is locally irregular if adjacent vertices ofG have different degrees. An edge-colouring Ï† ofG is locally irregular if each colour class of Ï† induces a locally irregularâ€¦ (More)

A graph is locally irregular if every two adjacent vertices have distinct degrees. Recently, Baudon et al. introduced the notion of decomposition into locally irregular subgraphs. They conjecturedâ€¦ (More)

Given a graph G, a sequence Ï„ = (n1, ..., np) of positive integers summing up to |V (G)| is said to be realizable in G if there exists a realization of Ï„ in G, i.e. a partition (V1, ..., Vp) of V (G)â€¦ (More)

A strong edge-colouring of a graph is a proper edge-colouring where each colour class induces a matching. It is known that every planar graph with maximum degreeâˆ† has a strong edge-colouring with atâ€¦ (More)

An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partitionâ€¦ (More)

A connected graph G with order n â‰¥ 1 is said to be recursively arbitrarily partitionable (R-AP for short) if either it is isomorphic to K1, or for every sequence (n1, ..., np) of positive integersâ€¦ (More)