A proper edge-coloring of a graph G is an assignment of colors to the edges of G such that
adjacent edges receive distinct colors. A proper edge-coloring defines at each vertex the set …

Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as
the set of colors of the edges which are incident with it. The palette index of a multigraph is …

An even cycle decomposition of an Eulerian graph is a partition of the edge set into even
cycles. We color the even cycles so as two cycles sharing at least one vertex receive distinct …

Let $ G $ be a connected graph with an even number of edges. We show that if the
subgraph of $ G $ induced by the vertices of odd degree has a perfect matching, then the …

Let G be a multigraph, C a set of colors and f: E (G)→ C a proper edge coloring of G. The
palette of a vertex v∈ V (G) is the set Sf (v)={f (vw): vw∈ E (G)}. The palette index of G is the …