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- W2020139369 abstract "We define NLC $_k^{mathcal{F}}$ to be the restriction of the class of graphs NLC k , where relabelling functions are exclusively taken from a set $mathcal{F}$ of functions from {1,...,k} into {1,...,k}. We characterize the sets of functions $mathcal{F}$ for which NLC $_k^{mathcal{F}}$ is well-quasi-ordered by the induced subgraph relation ≤ i . Precisely, these sets $mathcal{F}$ are those which satisfy that for every $f,gin mathcal{F}$ , we have Im(f ∘ g) = Im(f) or Im(g ∘ f) = Im(g). To obtain this, we show that words (or trees) on $mathcal{F}$ are well-quasi-ordered by a relation slightly more constrained than the usual subword (or subtree) relation. A class of graphs is n-well-quasi-ordered if the collection of its vertex-labellings into n colors forms a well-quasi-order under ≤ i , where ≤ i respects labels. Pouzet (C R Acad Sci, Paris Sér A–B 274:1677–1680, 1972) conjectured that a 2-well-quasi-ordered class closed under induced subgraph is in fact n-well-quasi-ordered for every n. A possible approach would be to characterize the 2-well-quasi-ordered classes of graphs. In this respect, we conjecture that such a class is always included in some well-quasi-ordered NLC $_k^{mathcal{F}}$ for some family $mathcal{F}$ . This would imply Pouzet’s conjecture." @default.
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- W2020139369 date "2010-09-15" @default.
- W2020139369 modified "2023-10-18" @default.
- W2020139369 title "Well-Quasi-Order of Relabel Functions" @default.
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- W2020139369 doi "https://doi.org/10.1007/s11083-010-9174-0" @default.
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