Strong edge-coloring of graphs with maximum degree 4 using 22 colors (Q2433734)

Erdős and Nesetril conjectured that every graph of even maximal degree \(\Delta\) can be strongly edge-colored by \(\frac54\Delta^2\) colors and if \(\Delta\) is odd by \(\frac14(5\Delta^2-2\Delta+1)\) colors. In this note the author gives a constructive contribution to the special case \(\Delta=4\).