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math.CO2021
Further Extensions of the Grötzsch Theorem
Hoang La, Borut Lužar, Kenny Štorgel
The Grötzsch Theorem states that every triangle-free planar graph admits a proper -coloring. Among many of its generalizations, the one of Grünbaum and Aksenov, giving -color…
math.CO2021★ 1 cited
3-facial edge-coloring of plane graphs
Mirko Horňák, Borut Lužar, Kenny Štorgel
An -facial edge-coloring of a plane graph is a coloring of its edges such that any two edges at distance at most on a boundary walk of any face receive distinct colors…
math.CO2021★ 12 cited
Strong edge colorings of graphs and the covers of Kneser graphs
Borut Lužar, Edita Mačajová, Martin Škoviera +1
A proper edge coloring of a graph is strong if it creates no bichromatic path of length three. It is well known that for a strong edge coloring of a -regular graph at least $2k-…