1 research outputs found
l-facial edge colorings of graphs
An l-facial edge coloring of a plane graph is a coloring of the edges such
that any two edges at distance at most l on a boundary walk of some face
receive distinct colors. It is conjectured that 3l + 1 colors suffice for an
l-facial edge coloring of any plane graph. We prove that 7 colors suffice for a
2-facial edge coloring of any plane graph and therefore confirm the conjecture
for l = 2