Brešar–Klavžar–Rall–Wash conjecture on subdivisions of subcubic graphs

From papers

For a graph GG, its 1-subdivision is obtained by replacing every edge with a path of two edges. The packing chromatic number χp(G)\chi_p(G), or PCN, is the smallest positive integer kk such that GG has a packing (1,2,,k)(1,2,\ldots,k)-coloring. Brešar–Klavžar–Rall–Wash conjecture. The 11-subdivision of every subcubic graph has PCN at most 55. Many advances have been made toward this conjecture, but the supplied status evidence says that it remained open since 2016.

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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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