König's line coloring theorem states that the edge chromatic number of any bipartite graph equals its maximum vertex degree. In other words, every bipartite graph is a class 1 graph.
An equivalent formulation is that the line graph of every bipartite graph is a perfect
graph. For every subgraph 
of a bipartite graph, the
chromatic number of 
is the edge chromatic
number of 
. By König's line coloring theorem, this equals the maximum vertex degree of 
. Because 
is a triangle-free graph,
the maximum vertex degree is also the clique number of 
.
