Haxell, Penny E.


Strong colorability ★★★

Author(s): Aharoni; Alon; Haxell

Let $ r $ be a positive integer. We say that a graph $ G $ is strongly $ r $-colorable if for every partition of the vertices to sets of size at most $ r $ there is a proper $ r $-coloring of $ G $ in which the vertices in each set of the partition have distinct colors.

Conjecture   If $ \Delta $ is the maximal degree of a graph $ G $, then $ G $ is strongly $ 2 \Delta $-colorable.

Keywords: strong coloring

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