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- W1989612647 abstract "We prove that every graph of minimum degree at least r and girth at least 186 contains a subdivision of K r +1 and that for r ⩾435 a girth of at least 15 suffices. This implies that the conjecture of Hajós that every graph of chromatic number at least r contains a subdivision of K r (which is false in general) is true for graphs of girth at least 186 (or 15 if r ⩾436). More generally, we show that for every graph H of maximum degree Δ ( H )⩾2, every graph G of minimum degree at least { Δ ( H ),3} and girth at least 166 log∣H∣ logΔ(H) contains a subdivision of H . This bound on the girth of G is best possible up to the value of the constant and improves a result of Mader, who gave a bound linear in ∣ H ∣." @default.
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- W1989612647 date "2002-11-01" @default.
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- W1989612647 title "Topological Minors in Graphs of Large Girth" @default.
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- W1989612647 doi "https://doi.org/10.1006/jctb.2002.2133" @default.
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