# Dvorak, Zdenek

## Star chromatic index of complete graphs ★★

Author(s): Dvorak; Mohar; Samal

**Conjecture**Is it possible to color edges of the complete graph using colors, so that the coloring is proper and no 4-cycle and no 4-edge path is using only two colors?

Equivalently: is the star chromatic index of linear in ?

Keywords: complete graph; edge coloring; star coloring

## Star chromatic index of cubic graphs ★★

Author(s): Dvorak; Mohar; Samal

The star chromatic index of a graph is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored.

**Question**Is it true that for every (sub)cubic graph , we have ?

Keywords: edge coloring; star coloring