Edge coloring of planar graphs which any two short cycles are adjacent at most once
By applying discharging methods and properties of critical graphs, we proved that every simple planar graph G  is of class 1 if ?(G)=6 ? ( G ) = 6 and any k-cycle is adjacent to at most one k -cycle for some k ( k = 3 , 4 , 5 ) .
edge coloring planar graph cycle maximum degree