Subdivisions of Kr+2 in graphs of average degree at least r + ε and large but constant girth
نویسندگان
چکیده
We show that for every ε > 0 there exists an r0 = r0(ε) such that for all integers r ≥ r0 every graph of average degree at least r + ε and girth at least 1000 contains a subdivision of Kr+2. Combined with a result of Mader this implies that for every ε > 0 there exists an f(ε) such that for all r ≥ 2 every graph of average degree at least r + ε and girth at least f(ε) contains a subdivision of Kr+2. We also prove a more general result concerning subdivisions of arbitrary graphs.
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