@article {IOPORT.05987727,
    author       = {Dellamonica, Domingos jun. and R\"odl, Vojt\v{e}ch},
    title        = {A note on Thomassen's conjecture.},
    year         = {2011},
    journal      = {Journal of Combinatorial Theory. Series B},
    volume       = {101},
    number       = {6},
    issn         = {0095-8956},
    pages        = {509-515},
    publisher    = {Elsevier Science (Academic Press), San Diego, CA},
    doi          = {10.1016/j.jctb.2011.04.002},
    abstract     = {Summary: In 1983 {\it C. Thomassen} [J. Comb. Theory, Ser. B 35, 129--141 (1983; Zbl 0537.05034)] conjectured that for every $k,g\in N$ there exists $d$ such that any graph with average degree at least $d$ contains a subgraph with average degree at least $k$ and girth at least $g$. A result of {\it L. Pyber}, {\it V. R\"odl} and {\it E. Szemer\'edi} [J. Comb. Theory, Ser. B 63, No.\,1, 41--54 (1995; Zbl 0822.05037)] implies that the conjecture is true for every graph $G$ with average $d(G) \geqslant c_{k,g} \log \Delta (G)$. We strengthen this and show that the conjecture holds for every graph $G$ with average $D(G) \geqslant \alpha (\log \log \Delta (G))^\beta$ for some constants $\alpha , \beta $ depending on $k$ and $g$.},
    identifier   = {05987727},
}