Majority 3-edge-coloring conjecture for graphs without pendant edges

A majority $3$-edge-coloring of a graph is an edge-coloring with three colors in which, at every vertex, the number of incident edges of its most frequent color is at most the number of incident edges having other colors. A graph is Class $2$ if its chromatic index exceeds its maximum degree. Majority 3-edge-coloring conjecture. Every graph $G$ without pendant edges admits a majority $3$-edge-coloring unless $G$ contains, as an induced subgraph, a Class $2$ graph $H$ with $\Delta(H)=3$ and with some vertices of $H$ having degree at most $3$ in $G$. The conjecture identifies subcubic Class $2$ subgraphs as the only obstruction to majority $3$-edge-colorability, extending the finite-graph conjecture to infinite graphs.