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- W4248566802 abstract "We consider the problem of the existence of universal countable C-free graphs with C a connected finite graph. For C a tree arising by from a path by adjunction of one additional edge we show that a universal countable C-free graph exists. We determine precisely the 2-bouquets C (i.e., unions of two complete graphs with jost one point in common) for which a universal countable C-free graph exists. We lay out some elements of a program for determining all the connected finite graphs C for which a countable universal C-free graph exists. One element of this program is the Tree Conjecture, which is now proved [2]. Our methods involve a mixture of model theory and combinatorics, with the Δ-system lemma playing a significant role. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 41–63, 2007" @default.
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- W4248566802 date "2007-01-01" @default.
- W4248566802 modified "2023-10-14" @default.
- W4248566802 title "Universal graphs with a forbidden near-path or 2-bouquet" @default.
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- W4248566802 doi "https://doi.org/10.1002/jgt.20245" @default.
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