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- W4385823801 abstract "Let G be a connected graph with maximum degree Δ≥3 distinct from KΔ+1. Generalizing Brooks’ Theorem, Borodin and independently Bollobás and Manvel, proved that if p1,…,ps are non-negative integers such that p1+⋯+ps≥Δ−s, then G admits a vertex partition into parts A1,…,As such that, for 1≤i≤s, G[Ai] is pi-degenerate. Here we show that such a partition can be performed in time O(n+m). This generalizes previous results that treated subcases of a conjecture of Abu-Khzam et al. (2020) which our result settles in full." @default.
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- W4385823801 date "2023-12-01" @default.
- W4385823801 modified "2023-10-15" @default.
- W4385823801 title "Partitioning into degenerate graphs in linear time" @default.
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- W4385823801 doi "https://doi.org/10.1016/j.ejc.2023.103771" @default.
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