Brešar, Klavžar, Rall, and Wash's packing chromatic number conjecture for subdivisions of subcubic graphs
Brešar, Klavžar, Rall, and Wash's packing chromatic number conjecture for subdivisions of subcubic graphs
Let be a subcubic graph, and let denote its subdivision, obtained by replacing each edge of by a path of length two. The packing chromatic number is the minimum for which has a packing -coloring, where a packing -coloring partitions the vertex set into classes such that the distance between distinct vertices in is at least . Brešar, Klavžar, Rall, and Wash's conjecture. The subdivision satisfies
This conjecture concerns whether the packing chromatic number is uniformly bounded for subdivisions of subcubic graphs; the source presents it as a conjecture following an earlier question by Gastineau and Togni, and does not state a resolution.
Sources & referencesView supporting material
Primary source
Alexandr Kostochka and Xujun Liu, “Packing (1,1,2,4)-coloring of subcubic outerplanar graphs”, arXiv:2005.04803 (2021).
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