Raspaud–Wang conjecture on partitioning triangle-free planar graphs

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Let GG be a finite simple triangle-free planar graph. A partition of GG into an independent set and a forest means that there is a partition (V1,V2)(V_1,V_2) of V(G)V(G) such that G[V1]G[V_1] is independent and G[V2]G[V_2] is a forest. Raspaud–Wang conjecture. Every triangle-free planar graph can be partitioned into an independent set and a forest. This would strengthen the known partition of triangle-free planar graphs into two forests; the conjecture is also independently attributed to Kawarabayashi and Thomassen in the surrounding discussion, while the paper presents it as an earlier conjecture of Raspaud and Wang.

References

Primary source

Guanwu Liu and Rongxing Xu, “Partitioning triangle-free planar graphs into a forest and a linear forest”, arXiv:2510.02038 (2025).

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