On the strong chromatic index of cyclic multigraphs (Q1962032)

The strong chromatic index \(\text{sq}(G)\) of a multigraph \(G\) is the smallest number of colours needed to colour the edges of \(G\) so that each colour class is an induced matching. The largest size of a submultigraph of \(G\) without any induced matching of size two is denoted by \(\eta(G)\). A cyclic multigraph is a multigraph whose underlying graph is a cycle. Results providing exact values or upper bounds for \(\text{sq}(G)\) where \(G\) is a cycling multigraphs are shown. The often involve the parameter \(\eta(G)\).