Brešar–Klavžar–Rall–Wash conjecture on subdivisions of subcubic graphs
Brešar–Klavžar–Rall–Wash conjecture on subdivisions of subcubic graphs
For a graph , its 1-subdivision is obtained by replacing every edge with a path of two edges. The packing chromatic number , or PCN, is the smallest positive integer such that has a packing -coloring. Brešar–Klavžar–Rall–Wash conjecture. The -subdivision of every subcubic graph has PCN at most . Many advances have been made toward this conjecture, but the supplied status evidence says that it remained open since 2016.
Progress summary
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Sources & referencesView supporting material
Primary source
Xinmin Hou, Xujun Liu and Xiangyang Wang, “Every connected subcubic graph except the Petersen graph is packing (1,1,2,2)-colorable”, arXiv:2603.23434 (2026).
Additional references
3 papers in this index state this conjecture (2022–2026). The statement above is taken from the most recent of them; the others are arXiv:2404.09337, arXiv:2209.09135.
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