What can we say about the total chromatic number of regular bipartite graphs that are not complete? Can we say they are of type 1[Total Colorable(no adjacent/incident elements have same color) by $\Delta+1$ colors where $\Delta$ is the maximum degree of the graph].
Can we say that regular, noncomplete bipartite graphs are formed by removing 1-factors recursively? If that be the case, then I think these graphs are of type 1. Any hints? Thanks beforehand.
On the other hand, can we use adjacent strong edge coloring, as mentioned here